Numerical Simulations of the Genesis of Hurricane Diana - American ...

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Numerical Simulations of the Genesis of Hurricane Diana (1984). Part II: Sensitivity of Track and Intensity Prediction CHRISTOPHER DAVIS National Center for Atmospheric Research,* Boulder, Colorado

LANCE F. BOSART University at Albany, State University of New York, Albany, New York (Manuscript received 14 June 2001, in final form 6 November 2001) ABSTRACT The authors examine numerous simulations that probe the dynamics governing the intensification and track of Tropical Cyclone Diana (1984) simulated in Part I. The development process is fundamentally dependent on a preexisting upper-tropospheric trough–ridge couplet. This couplet focuses mesoscale vertical motion that, in turn, produces lower-tropospheric potential vorticity (PV) anomalies, which form the seed for the tropical storm. Removal of this trough–ridge couplet from the initial conditions eliminates cyclogenesis. The simulated rate of development of Diana in the prehurricane phase depends principally on choices of cumulus parameterization, boundary layer treatment, sea surface temperature, and grid spacing. Simulations with cumulus schemes that allow more grid-scale precipitation on the 9-km grid exhibit unrealistic grid-scale overturning and slower intensification, primarily due to production of cyclonic vorticity anomalies at large radii. Use of an innermost nest with 3-km grid spacing, without a cumulus scheme, generally produces the intensification that agreed best with observations. Improvement over the control simulation stems from the emergence of convective downdrafts and a vertical motion spectrum that is less biased toward ascent. Consistent with recent work by Braun and Tao, the medium-range forecast model (MRF) planetary boundary layer (PBL) scheme produces a PBL that is too dry and too deep as winds intensify toward hurricane strength. Use of the Burk–Thompson scheme leads to excessive intensification with a 9-km grid spacing. Manual analysis of surface data produces a sea surface temperature (SST) field 18–28C warmer than is obtained from operational analysis. The warmer SSTs result in a storm that is about 27 hPa deeper after 60 h of integration. Storm track depends primarily on synoptic-scale structure at upper levels. Cumulus schemes that allow more grid-scale overturning enhance the anticyclonic outflow aloft. The outflow deforms the tropopause, building an anticyclone poleward of the storm and facilitating cutoff low formation equatorward of the storm. Using PV attribution, it is shown that these upper-level changes are responsible for an enhanced easterly steering flow and more westward storm track. Later initialization allows a better analysis of trough fracture, particularly the cutoff low and this also leads to a more westward storm track. Overall, despite the presence of a well-defined baroclinic precursor, the large sensitivity of track and intensity prediction to variations in model physics and initial conditions suggests that the development of Diana pushes the current limits of predictability.

1. Introduction a. Review of Part I The development of Hurricane Diana (1984) is notable for the important role of synoptic-scale, baroclinic precursors. As shown in Bosart and Bartlo (1991, hereafter BB), the storm begins as a subtropical baroclinic * The National Center for Atmospheric Research is sponsored by the National Science Foundation. Corresponding author address: Christopher A. Davis, National Center for Atmospheric Research, P.O. Box 3000, Boulder, CO 80307. E-mail: [email protected]

q 2002 American Meteorological Society

cyclone along a quasi-stationary front that had penetrated to remarkably low latitudes for early September. A cold-core upper-tropospheric trough is important for initiating baroclinic development, the precursor of tropical cyclogenesis. The modeling study of Davis and Bosart (2001, hereafter DB) captures the transformation of the baroclinic disturbance into a warm-core mesoscale vortex within the Pennsylvania State University–National Center for Atmospheric Research fifth-generation Mesoscale Model (MM5). In the simulation, weak baroclinic development begins as a cold-core upper-tropospheric trough moves off the Florida coast. Low-level warm advection, induced mainly by the upper-level disturbance initiates widespread precipitation and latent heating poleward of

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a quasi-stationary surface front. The heating produces numerous low-level positive potential vorticity (PV) anomalies. A dominant PV anomaly forms near the upshear (western) extremity of the lower-tropospheric frontal zone, amplified further through latent heating. The incipient vortex sweeps surrounding PV anomalies around itself, growing further by eddy vorticity fluxes as the anomalies are axisymmetrized. The transition to warm core occurs in about 8 h, from 1000 UTC 8 September to 1800 UTC 8 September. A 12-h period of quiescence follows during which the boundary layer and lower troposphere near the storm moisten. Renewed deepening in response to enhanced fluxes of water vapor from the ocean then occurs and the simulated storm reaches hurricane intensity by 1800 UTC 9 September. In the present paper, we examine the robustness of the mechanism advanced in DB of the transformation of the baroclinic disturbance into Tropical Storm Diana and eventually into Hurricane Diana. Dynamics of the initial development, featuring warm-core transformation, are examined using different treatments of physical processes (cloud physics, cumulus parameterization), variations in horizontal grid spacing (27 km, 9 km, and 3 km), different sea surface temperature (SST) analyses, and different initial conditions. Furthermore, we investigate the effect of these variations on the intensification of the storm to hurricane strength and on the track of Tropical Cyclone Diana. We will use the behavior of simulations with perturbed physical parameterizations, initial conditions, and SST, and the extensive body of existing knowledge regarding sensitivities in numerical simulations of tropical cyclones to obtain a more complete understanding of the essential processes involved in the development of Diana. b. Review of known sensitivities in numerical simulations

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mental shear (e.g., Gray 1982; DeMaria 1996), the mesoscale distribution of precipitation (e.g., Krishnamurti et al. 1998), presence of concentric eyewalls (e.g., Willoughby et al. 1982), dissipative heating in the core (Bister and Emanuel 1997; Zhang and Altshuler 1999), angular momentum fluxes resulting from interactions with midlatitude upper-level troughs (e.g., Riehl 1954; Molinari et al. 1998), and storm-induced sea surface temperature changes (e.g., Schade and Emanuel 1999). In addition, numerical simulations show considerable sensitivity to a number of factors that are entirely specific to models themselves as contrasted with the above factors, which are all believed to be true sensitivities in nature. A key sensitivity is horizontal grid spacing. Notable improvement of intensity prediction occurs as the grid spacing decreases to roughly the radius of maximum wind (RMW) or less (Walsh and Watterson 1997). Further sensitivity has been reported as the grid spacing is reduced below 10 km, such that simulations with resolutions of about 5 km are able to capture eyewall dynamics and better resolve storm outflow (Tripoli 1992; Liu et al. 1997; LeMarshall and Leslie 1999; Braun and Tao 2000). The effect of varying model grid spacing and physical parameterizations in finer-scale simulations (,10 km grid spacing) of tropical cyclone formation has not been investigated extensively. Based on simulations of mesoscale convective systems, we expect considerable sensitivity of tropical cyclone genesis to changes in grid spacing between roughly 2 and 20 km (Molinari and Dudek 1992) due to the lack of appropriate separation between resolved and parameterized scales of motion. In many simulations, an initial vortex is imposed, precluding any chance of simulating the earliest stages of tropical cyclogenesis and investigating the dynamics of the process and the related sensitivities, both natural and numerical. Much of the motivation for the present paper is to address this issue.

1) INTENSIFICATION A large body of research focuses on the sensitivity of the numerical treatment of air–sea heat and water vapor exchange in mature hurricanes. Based on work by Emanuel (1995, 1999) the intensification rate of hurricanes seems to depend on thermodynamic properties of the large-scale environment and the details of the air– sea exchange under the core of the storm. In particular, a key parameter is the ratio of the exchange coefficients of enthalpy and momentum; the larger this ratio, the faster the storm can intensify. Comparing simulations of Hurricane Bob (1991) using four different planetary boundary layer (PBL) schemes and five permutations thereof (a total of nine simulations), Braun and Tao (2000) show that the intensification rate is roughly proportional to this ratio calculated from each PBL formulation. Many other factors are suggested as being important in the intensification of hurricanes, including environ-

2) TRACK In recent years there have been numerous extensions of the basic concept of tropical cyclone motion resulting from beta gyres, the circulation around tropospheric PV anomalies arising from meridional advection of planetary vorticity. More generally, it is recognized that any azimuthal wavenumber one asymmetry in PV gives rise to a ventilation flow, which can effectively steer the tropical cyclone. In general, the largest gradients of PV are located at the tropopause and therefore, perturbation of these gradients can yield important flow anomalies. Studies by Wu and Emanuel (1993, 1995a,b) demonstrate how, by virtue of the large horizontal scale of the upper-level anticyclone, the circulation associated with this perturbation can penetrate through the troposphere and affect a deep layer. This anticyclone is partly due to the explicit material reduction in PV above the maximum heating and, perhaps more importantly, due to the

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rearrangement of tropopause PV due to the storm outflow. The notion of beta gyres and tropopause-based asymmetries acting together appears in Wang and Holland (1996a,b). As demonstrated by Shapiro and Franklin (1999), it is about as common for asymmetries within 1500 km of the storm center to govern its track as it is for anomalies outside 2000 km radius to be dominant. In the former category, the asymmetries responsible for steering are probably more strongly influenced by the storm itself, particularly the diabatic effects at high levels. As suggested by Dengler and Reeder (1997) and Henderson et al. (1999), the ability of numerical models to correctly simulate the outflow from a tropical cyclone bears directly on the upper-level asymmetries produced and hence on the ventilation flow. Henderson et al. (1999) suggest that part of the deficiency stems from inaccurate initial conditions. However, we will show that the uncertainties related to the parameterization of convective processes can have as large an effect on storm track as uncertainties in initial conditions. 2. Model description The modeling system used here is the PSU–NCAR model [MM5, Version 2; Grell et al. (1994)]. The domain configuration (Fig. 1) of the model is described in DB. The control simulation (CTRL) uses the mediumrange forecast model (MRF) planetary boundary layer scheme (Hong and Pan 1996), the numerical weather prediction explicit microphysics scheme (NEM; Schultz 1995), the Dudhia (1989) radiation scheme, and the Kain–Fritsch cumulus scheme (Kain and Fritsch 1993). For some simulations in the present study, a fourth domain is added (section 3e) wherein no implicit scheme is used. Numerous physics options are examined in the present paper in addition to the combination present in simulation CTRL. Because there is evidence for sensitivity of tropical cyclone prediction to a number of physical processes—for example, cumulus parameterization (Puri and Miller 1990), microphysics (Lord et al. 1984), and boundary layer processes (Braun and Tao 2000)—it is important to investigate the use of schemes with fundamentally different formulations. For implicit precipitation, we use the Betts–Miller– Janjic (Betts and Miller 1993) and Grell (1993) schemes. The former is a convective adjustment scheme wherein the reference equilibrium profile can be varied (see section 3d). The Grell (1993) scheme is an adaptation of the Arakawa–Schubert (1974) scheme with downdrafts added. Alternative explicit precipitation schemes include the Tao and Simpson (1993) scheme, a threecategory scheme (rain, snow, and hail) that has been applied extensively to tropical convection, and the socalled simple ice scheme (Dudhia 1989), which treats hydrometeors as rain at temperatures above freezing and as snow at temperatures below freezing.

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Two additional PBL schemes are used, the Burk– Thompson (1989) scheme and the Blackadar scheme (Zhang and Anthes 1982). The Blackadar scheme is a first-order closure scheme very similar in concept to the MRF scheme. We include it here because Braun and Tao (2000) demonstrated greater vertical mixing and a deeper boundary layer in the MRF scheme. The treatment of surface fluxes in the two schemes is nearly identical. The Burk–Thompson scheme predicts turbulent kinetic energy and employs a different surface layer scheme than used in the MRF scheme (Braun and Tao 2000). The reader is referred to Braun and Tao (2000) for a more detailed comparison of the formulations of the PBL schemes. The sea surface temperature analysis in CTRL is a blend of a manual analysis over the region of cyclogenesis (essentially over domain 3) with the operational navy SST analysis on coarser domains. The manual analysis methodology is outlined in section 3b and also in DB. A sensitivity study using only the navy SST (NAVSST) analysis is also performed. Table 1 summarizes the various sensitivity simulations considered in this paper. In all cases, two-way nesting is employed and initial conditions on nests are obtained from interpolation from the coarsest domain. Simulation CTRL was the focus of DB. For this simulation, we integrated three domains, with an innermost grid spacing of 9 km, all beginning at 1200 UTC 7 September 1984. 3. Intensification Figure 2 shows a set of time series of central sea level pressure for most of the simulations to be discussed in this section. The large spread about the observed deepening rate indicates the dramatic effect that variations in model physics, initial and boundary conditions can have. Later, we examine the reasons for the behavior of the simulations shown in Fig. 2. a. Modified upper-level PV In DB, it was found that the upper-level trough-ridge couplet was important for focusing the vertical motion and latent heating that allowed the initial spinup of Diana. Here we quantify the effect of the upper-tropospheric anomalies by removing them from the initial state and then integrating the forecast as before. Removal of a portion of the upper-level wind and temperature features is performed using a PV inversion technique (Davis and Emanuel 1991; Davis et al. 1996), wherein the nonlinear balance condition is imposed. The inversion is done on domain 1. We define a volume that encompasses the anomalous PV associated with the cold trough and downstream ridge in the upper troposphere (Fig. 3). The east and west boundaries of the region approximately span one zonal ‘‘wavelength’’ of the upper-level disturbance (about 2500 km). The northern

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FIG. 1. Domain configuration, including stationary location of domain 4 (3-km grid spacing, 151 3 151 points). The gray box defines the area from which anomalies of potential vorticity are defined.

boundary is chosen within the thinnest portion of the narrow positive PV anomaly that connects the stratospheric reservoir of high PV with the cold-core low to the south. The southern boundary is chosen to lie several hundred kilometers south of the anomalously large PV within the trough. The bottom of the volume is 600 hPa and the top is 150 hPa. This layer is chosen to encompass the deformed tropopause. Similar results are obtained if the bottom of the layer is as high as 400 hPa. On each pressure level, the PV at each i (the north– south grid index) is averaged zonally over grid indices j on the interval (j1 , j 2 ). The PV in this interval is replaced by a new PV field defined as

1

qi, j 5 qi, j1 1 2 when

( j # jc ) and

1

qi, j 5 qi, j2 1 2 when

2

j 2 j1 j 2 j1 1 Qi jc 2 j1 jc 2 j1 (3.1a)

2

j 2 jc j 2 jc 1 Qi j2 2 jc j2 2 jc

( j . jc ).

(3.1b)

Here, i and j are the indices for the ‘‘north–south’’ and ‘‘east–west’’ directions, respectively, consistent with the order of indices in MM5. The bounds on the averaging

area are (i1 , i 2 ) and (j1 , j 2 ), respectively, with a center at (i c , j c ). The PV averaged on (j1 , j 2 ) for each i is denoted Q i . The modified PV coincides with the original PV at the east and west end points of the averaging area and linearly transitions to the ‘‘zonally’’ averaged PV at the center. To perform the inversion, we adopt Neumann upper and lower boundary conditions for the streamfunction and geopotential fields and specify the potential temperature to be equal to the potential temperature of the initial condition of CTRL at 975 hPa and at 125 hPa, the lower and upper boundaries of the inversion domain, respectively. On lateral boundaries of domain 1, we specify geopotential and streamfunction equal to their values in the initial state of CTRL. The wind within the lowest 50 hPa in the perturbed initial condition is obtained by applying the same average fractional speed reduction and the same average angular rotation of the wind that was present in the control simulation initial state (DB). That is, if the average rotation over the lowest 50 hPa is 308 and speed reduction is 20% in CTRL, we apply these same corrections to the velocity in the perturbed initial condition. From Figs. 3a and 3b, the difference between initial conditions of the no-trough (NOPV) simulation and CTRL at upper levels is obvious. The cutoff low over

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TABLE 1. List of simulations. Simulation CTRL NOPV NAVSST BMJ1 BMJ2 GR EXP BT BKD BKD–BMJ 2D 4D21 4D24 4DI08 I07 I08

MinDx 9 9 9 9 9 9 9 9 9 9 27 3 3 3 9 9

km km km km km km km km km km km km (at 21 h) km (at 24 h) km (at 12 h) km km

Initial conditions 12Z 12Z 12Z 12Z 12Z 12Z 12Z 12Z 12Z 12Z 12Z 12Z 12Z 12Z 00Z 00Z

7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 8

Sep Sep (no trough) Sep Sep Sep Sep Sep Sep Sep Sep Sep Sep Sep Sep Sep Sep

Florida in CTRL does not appear in the initial conditions of NOPV. In the lower troposphere, in addition to weaker cyclonic circulation implied by the sea level pressure field in NOPV, the warm advection region to the east of Florida is nearly eliminated (not shown). In NOPV, there is little to focus the vertical motion within the baroclinic zone. Examination of the 36-h forecast in each simulation (Figs. 4a and 4b) reveals that the weak inverted trough present initially in NOPV migrates westward to the Gulf of Mexico over 36 h, but does not develop a notable surface signature, whereas there is a well-defined storm in CTRL that had reached tropical storm strength. Note that in NOPV, the water vapor mixing ratio is unaltered compared to CTRL. Hence, since the low-level temperature is also the same, the thermodynamic stability of the atmosphere is very similar to that in CTRL.1 Indeed, convection occurs in NOPV, but it is not organized and localized to the extent seen in CTRL. Our interpretation is that the low-level inverted trough is not a sufficiently strong disturbance to organize convection on its own, so the system does not amplify.

PBL–SFC

Cumulus

MRF MRF MRF (navy SST) MRF MRF MRF MRF Burk–Thompson Blackadar Blackadar MRF MRF MRF MRF MRF MRF

Kain–Fritsch Kain–Fritsch Kain–Fritsch Betts–Miller–Janjic (ML) Betts–Miller–Janjic (Trop) Grell none (D-3 only) Kain–Fritsch Kain–Fritsch Betts–Miller–Janjic (ML) Kain–Fritsch none (D-4 only) none (D-4 only) none (D-4 only) Kain–Fritsch Kain–Fritsch

The navy SST analysis does not capture the narrow tongue of warm SSTs extending northward to the east of Florida that is apparent in Fig. 1 of DB. The sea state preceding the development of Diana was probably highly disturbed owing to the steady northeasterly surface winds of about 15 m s 21 present in the area where many ship and buoy observations were taken. Hence, it is not likely that the difference between navy and analyzed SST is due to the presence of a shallow layer of warmer water residing on the surface, as can occur in relatively calm conditions. The difference could be due to the influence of climatological information and the coarseness of the navy analysis. The cooler SSTs in NAVSST result in a significantly weaker development as compared to CTRL such that by 60 h, the central pressure in NAVSST is 27 hPa higher than in CTRL. The evolution of the NAVSST simulation is broadly similar to CTRL in terms of the timing of development and the overall track. As can be seen from Fig. 5, beginning near 33 h, the end of the first deepening phase, there is a high correlation between the u e difference at the storm center, expressed as a

b. SST As described in DB, hand analyses supplement the navy’s operational SST field over the region of cyclogenesis (see Fig. 1 of DB). Because of the subjectivity of the analysis, it is reasonable to investigate the sensitivity to using this analysis as compared with the unsupplemented navy analysis. The navy SSTs under the storm are almost uniformly 18–28C lower than in our analysis in the region where Diana developed (Fig. 5). 1 Changes in the upper-tropospheric PV will generally change the mid- and upper-tropospheric temperatures and therefore alter the convective available potential energy (CAPE). However, it appears that differences in CAPE between CTRL and NOPV are small in the present case, and differences are particularly small between the upperlevel trough and ridge where much of the convection occurs.

FIG. 2. Minimum sea level pressure time series for simulation CTRL and selected sensitivity simulations. Observations are indicated with filled circles.

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FIG. 3. Sea level pressure and 300-hPa geopotential heights at 0 h (1200 UTC 7 Sep) for (a) NOPV and (b) CTRL. The contour interval is 2 hPa for sea level pressure (thin lines) and 20 m for 300-hPa geopotential height (heavy lines). Lighter shading denotes PV on the 340 K isentropic surface greater than 1.5 PVU (1 PVU 5 10 26 m 2 K kg 21 s 21 ) and darker shading indicates PV greater than 4 PVU.

theoretical pressure deficit Dp(hPa) 5 2.5D u e (K), (Malkus and Riehl 1960) and the simulated sea level central pressure difference. One expects this result for mature hurricanes (Malkus and Riehl 1960; Emanuel 1986), but here, the correlation exists for a storm of modest intensity. In the version of MM5 used herein, SST does not vary in time, therefore, the effects of oceanic responses to atmospheric forcing on storm intensity cannot be examined. Coupled atmosphere–ocean modeling studies of hurricanes generally show that upwelling caused by

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FIG. 4. Near-surface winds (40 m MSL) and 3-h accumulated precipitation valid at 36 h (0000 UTC 9 Sep) for (a) NOPV and (b) CTRL.

storm-induced surface stresses weakens the hurricane in proportion to the cooling of the ocean under the core (Bao et al. 2000; Shay et al. 2000). The amount of cooling varies inversely as the depth of the thermocline and the translational speed of the storm. Application of a coupled model is beyond the scope of the present study, however, given the relatively slow movement of Diana, we can speculate that inclusion of the upwelling effect would reduce the intensity of the simulated

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FIG. 5. Time series of central sea level pressure difference (NAVSST 2 CTRL) between CTRL and NAVSST (heavy solid line), an estimate of this difference using the central u e difference (thin solid line), and the SST difference (CTRL 2 NAVSST; dashed).

storms. Given the disturbed sea state that preceded development, and the fact that the warm SSTs were within the Gulf Stream where they were not likely associated with shallow, warm water susceptible to cooling following an increase in surface winds, it is possible that the reduction of intensity would be modest. c. PBL schemes Because the fluxes of water vapor from the ocean are the critical source of energy for the developing hurricane, and because the PBL scheme is the primary means

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by which the fluxes are distributed vertically, it is important to examine the sensitivity of the simulations to different PBL schemes or variations of parameters within schemes. Herein, we contrast simulation CTRL with simulation BKD, using Blackadar scheme (Zhang and Anthes 1982), and simulation BT, using the Burk– Thompson scheme (Burk and Thompson 1989). In simulation BT the storm deepens faster and to a greater intensity than with the MRF scheme (Fig. 2). The intensity of the storm in BKD is only 3 hPa deeper than in CTRL after 60 h, and the timing of the intensification is also very similar to that in CTRL. Consistent with these results, Braun and Tao (2000) also find that the Burk–Thompson scheme produces a storm of greater intensity than either the MRF or Blackadar schemes. Also as shown by Braun and Tao (2000), the boundary layer in the MRF scheme tends to become the driest and deepest as the storm reaches hurricane strength (Fig. 6). Ultimately, the azimuthally averaged surface humidity falls below 70% outside a radius of 100 km (Fig. 6d). The Burk–Thompson scheme maintains the humidity at outer radii at about 85%, a seemingly more reasonable value (Fig. 6c). The Blackadar schemes yields near-surface humidities that are similar to those produced by the Burk–Thompson scheme, averaging 80% to 85% at radii greater than 100 km (not shown). During the genesis phase, however, the differences between the schemes are in the same sense, but smaller (Figs. 6a,b). Moreover, it is not clear, based on surface

FIG. 6. Radius-height depictions of relative humidity for (a) BT simulation at 27 h, (b) CTRL at 27 h, (c) BT at 54 h, and (d) CTRL at 54 h.

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FIG. 7. Observations of dewpoint depression adapted from BB and superposed on storm-relative grid. Symbols indicate time of observation. Range rings are spaced at 100-km intervals.

observations which scheme is better. The surface observations of dewpoint depression (taken from BB, their Fig. 9) are composited over a 12-h period in a stormrelative coordinate system (Fig. 7). Three times are included: 1200 and 1800 UTC 8 September and 0000 UTC 9 September. Coastal observations are used at 0000 UTC 9 September when Diana was approaching Cape Canaveral, but inland observations are not used. No obvious trend versus time or radius is apparent in Fig. 7 (Table 2). Two observations occurred within rainbands, but generally, the dewpoint depression is 28–48C, corresponding to a relative humidity range of approximately 85% to 80%, respectively (Table 2). This range is between the humidities in CTRL (70%–75%) and BT (about 90%), and close to the near-surface humidity found in BKD (not shown). Braun and Tao (2000) also note that in addition to having a more moist PBL than the MRF scheme, the ratio of moist enthalpy flux coefficient (C K ) to the frictional drag coefficient (C D ) is about unity in the Burk–

Thompson scheme and only about 0.7 in the MRF and Blackadar schemes. Emanuel (1995) shows that the ultimate storm intensity should depend on the ratio C K / C D . Thus, it appears that there are two factors contributing to enhanced development in BT: (1) the shallower and moister PBL, arising from less vertical mixing than in the MRF scheme, which implies that a given flux of water vapor can more easily increase u e in the boundary TABLE 2. Observations of humidity vs radius from storm center. Here, s is the standard deviation of dewpoint depression within each 50-km radius bin. r (km)

T d (8C)

RH (%)

s (8C)

0–50 50–100 100–150 150–200 200–250 250–300

2.7 2.5 3.2 3.8 3.2 3.4

85 86 83 80 83 82

0.8 1.6 0.5 0.9 1.3 1.4

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layer, and (2) the greater value of C K /C D than in either the Blackadar or MRF schemes, which implies a greater amount of latent energy available for intensification relative to frictional dissipation. In view of the similarity of storm intensity in simulations BKD and CTRL, it would appear that the treatment of surface exchange exerts a greater influence on the intensity than the mixing within the PBL. d. Cumulus schemes The use of an implicit precipitation scheme on the 9km grid may be regarded as questionable from a physical point of view (Molinari and Dudek 1992). In this section, we examine simulations with the Betts–Miller– Janjic (Betts and Miller 1993) and Grell (Grell 1993) schemes, and also examine a simulation in which the implicit scheme withheld on the 9-km grid. A commonly used scheme in the Tropics is the Betts– Miller scheme (Betts and Miller 1993), especially for tropical cyclone simulations (e.g., Liu et al. 1997). The particular version of the scheme used here is obtained from the National Centers for Environmental Prediction and is known as the Betts–Miller–Janjic scheme (hereafter BMJ). This scheme is a convective adjustment scheme rather than a model of cloud evolution as is the Kain–Fritsch scheme. Thus, it is simpler and much of the sensitivity involves the choice of reference profile toward which the atmosphere is adjusted and the timescale over which adjustment occurs. The primary parameters to be adjusted are saturation pressure deficits for air near cloud base, the freezing level, and near the tropopause along with a parameter that controls how closely the reference profile follows a moist adiabat. The pressure deficit is the change in pressure required to bring a parcel to saturation. Typically, for tropical applications, the stability parameter is nearly unity, meaning that the reference profile exhibits a moist adiabatic lapse rate. We use two sets of profiles, one perhaps more representative of midlatitudes, the other more representative of the deep Tropics. The former is defined by the pressure deficits (dp B , dp 0 , dp T ) 5 (238.75, 258.75, 218.75) in hPa with a stability parameter of 0.9. Subscripts B, 0, and T refer to cloud base, freezing level, and tropopause, respectively. The tropical profile derives from Betts and Miller (1993); (dp B , dp 0 , dp T ) 5 (220.0, 240.0, 220.0) in hPa with a stability parameter of 1.0. As the present case is a hybrid tropical–extratropical development, it is not clear a priori which set of parameters is more appropriate. The simulation with ‘‘midlatitude’’ parameters (BMJ1) produces the better storm intensity and track but the tropical parameters (BMJ2) produce what appeared to be more plausible rainfall rates (roughly half of the rates in simulation with midlatitude parameters). Since rainfall is not measured, this is partly conjecture. Peak hourly rainfall amounts with midlatitude param-

FIG. 8. Hourly rainfall, averaged over a 153 3 153 km2 area centered on the storm for BMJ and CTRL, expressed as mm (grid point) 21 . The heavy solid curve represents explicit precipitation from CTRL (CTRLexp ); the heavy dashed curve is explicit precipitation from BMJ1 (BMJexp ); thin lines denote implicit precipitation, solid for CTRL (CTRLcp ), dashed for BMJ (BMJcp ). Curves for CTRL begin later due to difficulties in locating center prior to 16 h (0400 UTC 8 Sep).

eters are in excess of 100 mm. This rate is conceivable for individual convective cells, but because entire mesoscale regions experience this rainfall in the simulation, the validity of the rainfall prediction is highly questionable (Venugopal et al. 1999). In BMJ1, the intensity of the storm is reduced relative to CTRL and the storm is weaker than observed (Fig. 2). During the early development of the storm (prior to 1800 UTC 8 September), the rainfall rates are significantly larger in BMJ1 (Fig. 8). The peak rainfall rate occurs in BMJ1 between 0600 and 1200 UTC 8 September and was about 1.7 times the maximum rainfall rate in CTRL. The majority of the rainfall during these enhanced periods is produced by the explicit precipitation scheme. The rainfall due to the implicit scheme is approximately 1 mm h 21 (averaged over the 17 3 17 gridpoint box, or about 23 000 km 2 ). The apparent contradiction between the much heavier rain rates and the weaker development in BMJ1 relative to CTRL can be explained by considering the spatial distribution of precipitation and associated vorticity and potential vorticity anomaly generation relative to the storm center. Although the precipitation in BMJ1 from 21–27 h (0900 to 1500 UTC 8 September) is heavier than in CTRL, it is distributed in an elongated strip along a southwest–northeast axis and the resulting 900 hPa PV shows a similar distribution (Fig. 9). Over the next 6 h, the precipitation and PV fields in BMJ1 show less linear structure (Fig. 9c), but there is still a tendency for heavy precipitation and strong anomalies further from the storm center than in CTRL (Fig. 9d). In simulation CTRL, most of the precipitation at large radii is produced by the Kain–Fritsch scheme (not shown). Because the implicit precipitation is generally light, its associated latent heating has more subtle effects on the

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FIG. 9. 6 h, storm-centered precipitation, 900-hPa PV contours (1, 2, 4, and 8 PVU) and 900-hPa winds at every fourth grid point from domain 3 for (a) 27 h from BMJ1, (b) 27 h from CTRL, (c) 33 h from BMJ1, and (d) 33 h from CTRL. Zero and negative PV not shown.

pressure and wind fields than the effect of the locally heavy explicit precipitation in BMJ1. Numerous studies on the intensification of vortices from diabatic heating (e.g., Schubert and Hack 1982) show that heating at large radii reduces spinup efficiency. In addition, work by Montgomery and Enagonio (1998) further supports the concept of a critical radius beyond which cyclonic PV anomalies do not intensify

the mean tangential circulation when they are axisymmetrized. The effect of vorticity anomalies at various radii can be quantified using similar vorticity flux diagnostics as were shown in DB (their Fig. 14). Briefly, the change in azimuthally averaged, tangential wind is caused mainly by two contributions, the vorticity flux due to the symmetric radial circulation, u h and the eddy flux

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FIG. 10. Radial profiles of eddy-induced angular momentum changes from CTRL (heavy solid) and BMJ1 (dashed). All quantities represent averages from 21 to 36 h and from roughly 0 to 2 km MSL.

u9z9 . Here u is the radial wind, h is the absolute vorticity, and z is the relative vorticity. Overbars and primes denote the azimuthal average and deviations from it, respectively. Here, we highlight the differences due to the eddy contribution. To more consistently compare accelerations at different radii, we examine the the change in angular momentum, r]y /]t, where y is the tangential wind. The curves in Fig. 10 illustrate that the eddy-induced accelerations are weaker and displaced to greater radii in BMJ1 than in CTRL. In particular, the contribution from eddy fluxes in BMJ1 is larger for r . 200 km. It appears that an important contribution to the smaller intensification rate in BMJ1 relative to CTRL is the production of PV anomalies and an associated increase of tangential wind at larger radii than in CTRL. In performing simulation BMJ2 we attempt to correct for the excessive precipitation rates in BMJ1 by using a thermodynamic profile with less potential instability. The result is more plausible rainfall, but a storm of only half the intensity as in BMJ1 (not shown), even further from what is observed. We perform three other simulations, one with the Grell (1993) scheme (GR) and another with no cumulus scheme (EXP). A third simulation uses the Blackadar PBL scheme and the Betts–Miller-Janjic cumulus scheme (BKD–BMJ1). All three simulations produce notably weaker development than CTRL or BMJ1. The evolution in GR and EXP is qualitatively similar. The dominance of the explicit scheme in each (by definition in EXP) produces excessive local perturbations to the pressure and wind fields near each major grid-scale overturning. Similar behavior is noted in many previous studies where the explicit precipitation scheme assumed a dominant role at coarse resolution (Kuo et al. 1996). It appears that 9-km grid spacing is too coarse to forgo an implicit scheme in this case. Simulation BKD–BMJ1 produces only a weak, synoptic-scale cyclone. Localized heavy rainfall, governed by the explicit precipitation scheme, occurs within the

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first few hours of the simulation. In response, several weak mesoscale vortices form, but none amplify. Strong, grid-scale subsidence dries out mesoscale areas of the lower troposphere and appears to inhibit the organization of convection and latent heating. To summarize, differences between CTRL, using the Kain–Fritsch scheme, and other simulations result from (a) the activity of the scheme, that is, the frequency with which it triggers, and (b) the imposed temperature and water vapor tendencies once activated. Judging from the area coverage of parameterized rainfall, the Kain– Fritsch scheme triggers more often than any of the other schemes. The trigger function in the Kain–Fritsch scheme includes a buoyancy contribution that is positive if there is grid-resolved upward motion at the lifted condensation level (Fritsch and Kain 1993). Other schemes simply check for buoyancy by lifting parcels representative of individual layers. Given widespread upward motion induced by frontal ascent and the initial presence of minimal convective inhibition, the Kain– Fritsch scheme becomes widely active. The Kain– Fritsch scheme is effective in stabilizing the lower troposphere to parcel ascent, but maintains marginal conditional instability for lifted layers. We believe this is why the explicit precipitation is confined to the front and, later, the eyewall in CTRL, where strong mesoscale lifting persists. The formation of lower-tropospheric vorticity anomalies is similarly confined to regions where the anomalies already exist, and amplification occurs more readily. In the other simulations, the cumulus scheme is not active enough to adjust the troposphere given the continued destabilization due to mesoscale lifting and input of latent energy from the ocean beneath. The result is a less confined distribution of gridscale precipitation and latent heating. Multiple vorticity anomalies form on marginally resolved scales, separated by distances too great for merger on the timescale of the simulation. e. Grid spacing One of the more notable sensitivities in our simulations is that of variations in horizontal grid spacing and the associated change in physical processes. We consider both coarser grid spacing (27 km) and finer grid spacing (3 km), the latter requiring a restricted (and sometimes translating) domain because of computational constraints. At 3-km grid spacing we forgo an implicit cloud scheme. 1) 27-KM

GRID SPACING

In the simulation with a grid spacing of 27 km (denoted 2D), we retain the same physical parameterizations as in CTRL. Arguably, the parameterizations (e.g., Kain–Fritsch) are more appropriate at this grid spacing. In simulation 2D, the storm is considerably weaker than CTRL and also the observed storm (Fig. 2). We believe

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FIG. 11. Minimum sea level pressure for CTRL and the three simulations using a fourth domain.

that this deficiency stems from a lack of grid-scale saturation within the frontal zone and the associated generation of mesoscale PV anomalies in the lower troposphere. Thus, the initial spinup of a mesoscale vortex is delayed and the vortex that eventually forms is weaker than its counterpart in CTRL. The storm is therefore not able to undergo appreciable self-amplification through air–sea interaction before it drifts over cooler water. 2) 3-KM

GRID SPACING

The nest with 3-km grid spacing is inserted into domain 3 (Fig. 1). When inserted into simulation CTRL, it remains fixed through 60 h. When inserted into I08, the simulation with identical physical parameterizations as CTRL but begun at 0000 UTC 8 September, the greater movement of the storm requires that we allow domain 4 to move in a series of discrete jumps following the storm. Each jump is about 30 km and a total of about 5 jumps are needed to contain the storm. In all cases, the fourth domain consists of 151 grid points in each horizontal direction. In the section that follows, the suffix -4D is added to the names of CTRL and I08 to denote that they were run with four domains. The initialization time of domain 4 proves to be important. We delay the start of domain 4 to allow the model to spin up features on domain 3 and thereby help determine the placement of the nest. Two nest initialization times will be considered, 0900 UTC 8 September (simulation denoted CTRL-4D21) and 1200 UTC 8 September (simulations CTRL-4D24 and I08-4D). The significance of initializing at these two times is that they bracket a major eruption of convection on the mesoscale, seen both in the observations and in CTRL (DB). Note that the fourth domain in I08-4D is initialized at the same time as in CTRL-4D24, but only 12 h after the start of the three-domain integration (I08) from which it is spawned. Figure 11 shows the time series of minimum sea level pressure (SLP) for each of the simulations with a fourth

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domain, along with simulation CTRL and the observations as in Fig. 2. All simulations with a 3-km nest show a weaker storm than their counterpart simulations using a minimum grid spacing of 9 km. Also, earlier initialization of domain 4, relative to the start of the simulation, results in a weaker storm. Some spinup of domain 3 (with both implicit and explicit schemes) appears necessary prior to the introduction of domain 4 (explicit only) for accurate intensity prediction. One possible interpretation of this result is that 3-km grid spacing is not quite fine enough to properly treat the tropical convection, at least not until mesoscale vertical motion becomes more well organized after an initial cyclogenesis period. In the remainder of the section, we focus on simulation CTRL-4D21 and contrast it with CTRL. From Fig. 12, it can be seen that the three-domain simulation produces a fairly symmetric vortex (Figs. 12a and 12c) whose maximum winds at 900 hPa are about 42 m s 21 , contrasted with a maximum speed in CTRL-4D21 of 30 m s 21 . The four-domain simulation produces maximum winds on the southeast flank of the storm (Fig. 12d) in agreement with reconnaissance observations near this time (Bosart and Bartlo 1991, see their Fig. 12c). As expected, considerable structure exists in the four-domain simulation that is not present at coarser resolution. While both simulations reveal banded precipitation structures, bands in CTRL-4D21 are more numerous and narrower. The amplitude of asymmetries apparent in Fig. 12b characterizes other times in CTRL-4D21. We show four consecutive hourly depictions of rainwater mixing ratio and sea level pressure in Fig. 13. Beginning at 1900 UTC 9 September, a poorly organized mesoscale rainband takes shape on the southeast flank of the storm. The rainband organizes as it is advected by the symmetric circulation past the northeast quadrant of the storm. Because the storm is moving northward, this quadrant is the right-front quadrant, noted by other investigators as the locus of heavy rainfall in other cyclones featuring significant asymmetries (Burpee and Black 1989). However, because the deep tropospheric shear vector, averaged within 100 km of the storm center, points toward the east-northeast during this period (magnitude of about 0.8 3 10 23 s 21 , not shown), the area of intensification of the rainband is almost directly downshear. The outer portion of the rainband appears to dissipate quickly, whereas the portion of the band nearer the center continues to rotate cyclonically and eventually dissipates over the southern flank of the storm following 2200 UTC. Near and within the radius of maximum wind (40– 50 km), the rainwater maxima are generally coincident with local minima in sea level pressure and enhanced cyclonic circulation on scales of only about 15–20 km. This behavior contrasts markedly with that outside the RMW where precipitation anomalies are typically associated with locally higher sea level pressure. The im-

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FIG. 12. Comparison of CTRL and CTRL-4D21 at 56 h (2000 UTC 9 Sep; (a) and (c) show sea level pressure (1 hPa interval) and rainwater at the lowest model level, (b) and (d) show 900-hPa PV and wind (negative PV omitted). Short wind barbs indicate wind speed of 2.5 m s21, long barbs 5 m s21, and pennants 25 m s21.

plication is that convection outside the RMW produces cooling of the boundary layer, presumably through negatively buoyant downdrafts, while convection near the center produces downdrafts with reduced negative

buoyancy. This is consistent with the radial profile of azimuthally averaged and time-averaged relative humidity (Fig. 14), which reveals that the mean humidity in the layer between 0.5 and 4 km MSL is about 90%

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FIG. 13. Evolution of sea level pressure and rainwater at lowest model level from CTRL-4D21. Shown are four successive times at an hourly interval beginning at 1900 UTC 9 Sep (55-h simulation). Annotations V1 and V2 refer to individual subcyclone-scale vortices.

near the RMW but below 80% outside a radius of 150 km. The lack of cooling associated with the inner-core convection allows the dominant change in the mass and wind field (see Fig. 13) to be lower pressure coincident with a cyclonic flow anomaly. In addition, the greater absolute vorticity inside the RMW would enhance the vortex stretching and amplification rate of the mesovortices closer to the storm center.

Studies of intense hurricanes reveal the possibility of mesovortices on the eyewall forming from barotropic instability (Schubert et al. 1999). However, since the radial gradient of absolute vorticity is monotonic (not shown), such an explanation is unlikely in the present case. The vortices seen here appear to be fundamentally tied to latent heating in convective bursts near the eyewall. Similar mesovortices, collocated with

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FIG. 14. Time, azimuthally and vertically averaged relative humidity for CTRL and CTRL-4D21. Averaging time is from 51–60 h and averaging depth is from about 500 to 4 km MSL.

reflectivity maxima, have been observed in developing tropical storms (Stewart and Lyons 1996) and in mature hurricanes (Marks and Houze 1984). However, the observed structures were about half the diameter of those in our simulation and evolved more rapidly. Part of the discrepancy may be due to the use of 3-km grid spacing, only about half the RMW of the observed mesovortices. These mesovortices proceed around the core, typically making about 1 revolution before decaying. As each one decays, it strengthens the symmetric vortex. In the case of 4D24, the anomalies are strong enough that they produce a steplike structure in time trace of minimum sea level pressure (Fig. 11), wherein each step represents a complete cycle of eddy formation and eddy decay with a concomitant increase in the symmetric circulation. There is an overall qualitative similarity with the idealized simulations of Montgomery and Enagonio (1998, 2001) and Mo¨ller and Montgomery (2000), wherein the axisymmetrization of localized anomalies of PV intensifies the cyclone. The roughly continuous sequence of mesovortex formation and decay in favor of the symmetric circulation allows a nearly steady intensification. That is not to say that in the absence of vortices the storm would not intensify, but rather, that the formation of strong convective asymmetries appears to be the preferred mechanism of development in this case. This mechanism is clearly less pronounced at coarse resolution once the storm approaches hurricane strength. We focus on the structure of a particular mesovortex in Fig. 15. The vortex is coherent from the surface through 850 hPa and is detectable up to 500 hPa, although it exhibits considerable vertical tilt in the lower and middle troposphere toward the northwest with height (locally downshear with respect to the tangential wind in this quadrant of the vortex). The structure is warm core and the circulation is strong enough that the wind locally becomes nearly calm. From Fig. 13, it can be inferred that another mesoscale vortex forms near

FIG. 15. (a) Sea level pressure, wind at lowest model level (40 m MSL) and 900-hPa PV valid 2000 UTC 9 Sep (56 h); (b) 850-hPa temperature and wind at the time shown in (a). See Fig. 13 for subdomain location.

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FIG. 16. Histograms of vertical motion (w) and the correlation of w at 3 km MSL with absolute vorticity h averaged over the lowest 3 km MSL. (a) and (c) Statistics from a 9-km storm-centered grid (CTRL) that is 225 3 225 km2. (b) and (d) Statistics from the same area as in (a) and (c) but from domain 4 of CTRL-4D21 and after averaging w and wh over 3 3 3 subdomains on the 3-km grid (see text for details). Units for w are m s 21 and for wh are 10 24 m s 22 . Statistics have been accumulated from 45 to 60 h for both simulations. Bin number refers to ranges of w and wh shown in legend at lower right.

the RMW and reaches comparable strength to that shown in Fig. 15. A central issue is why the simulations with a higherresolution domain each produce a weaker storm than CTRL. Some insight is gained by a statistical analysis of vertical velocity and the stretching term in the vorticity equation. As was apparent from Fig. 15 in DB, the stretching term dominates the vorticity tendency. We analyze vertical velocity at the level nearest 3 km MSL (w H ) and the product of w H and absolute vorticity averaged over the layer beneath 3 km MSL (h H ). Because the vertical velocity vanishes at the ground, the product w H h H /H, where H is the physical depth of the layer (a

constant), is an approximation to the stretching term in the vorticity equation and represents the rate of increase of a vertical component of vorticity within the layer from the surface to about 700 hPa. Figure 16 shows frequency histograms for both vertical motion and the stretching term obtained as follows. The vertical motion and wh correlation are averaged over contiguous 3 3 3 grids on domain 4 within a square area of 153 km on a side centered on the storm. For the three-domain simulation, w and wh are computed at each grid point within the same area. By coarsening the fields on domain 4 by a factor of 3, the resulting quantities can be compared directly because they both rep-

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resent averages over a 9 km 3 9 km area. The histograms of w and wh shown in Fig. 16 represent a summation from 45 to 60 h. The bins, each representing a range of values for w H and w H h H (the latter scaled by 10 4 ), are constructed to increase geometrically in width so as to de-emphasize the tendency for the quantities to cluster about zero. From Fig. 16, it is clear that the domain with 9-km grid spacing produces more numerous and stronger updrafts with fewer and weaker downdrafts than on the 3km grid. Note the skewness of the distribution for the 9-km grid, accentuating positive vertical velocities, and the relatively symmetric appearance of the histogram for the 3-km grid, revealing less of a bias in w H . While the consistently higher absolute vorticity present in CTRL (9-km grid) is partly responsible for the systematically greater vortex stretching, it appears that much of the discrepancy in the vortex stretching term (compare Fig. 16b with Fig. 16d) is accounted for by the differences in vertical motion between the two simulations. In fact, the ratio of the time-averaged and areaaveraged vertical velocity, 16 cm s 21 for CTRL and 8 cm s 21 for CTRL-4D21, is about the same as the ratio of the stretching term in the two simulations. Without a complete vorticity budget it is not possible to quantify the effects of the differing probability distributions of vertical velocity on storm intensification, but the qualitative inference is that the biased distribution of w in CTRL is the source of the greater intensification rate and it may be physically interpreted as a relative absence of convective downdrafts and an excess of upward motion. The differences in vertical motion spectra are consistent with the differences in lower-tropospheric humidity seen in Fig. 14 wherein CTRL-4D21 was systematically drier than CTRL near the RMW. Although a clear cause and effect is not evident, the presence of more numerous and intense downdrafts would be expected in an environment of lower humidity and would tend to maintain such a humidity state. However, the more vigorous downdrafts in CTRL-4D21 at 3 km MSL do not appear to penetrate into the boundary layer, judging from the nearly identical profiles of u e within the PBL in each simulation. The reduced humidity in the storm center in CTRL (inside a radius of about 30 km) is probably a consequence of the more well-defined eye due to a greater storm intensity in that simulation as compared to CTRL-4D21. Weisman et al. (1997), in a study of squall line simulations with horizontal grid spacing varying from 1– 12 km, note the tendency for weaker downdrafts and stronger updrafts at coarser resolution (8–12-km grid spacing) as compared to the coarsened vertical motions from the high-resolution simulations (1–4-km grid spacing). The stronger updrafts are attributed to improper treatment of nonhydrostatic effects at coarse resolution. In our case, a 9-km grid spacing is still within the hydrostatic regime, whereas 3-km grid spac-

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ing should incorporate nonhydrostatic effects which limit vertical motion through the creation of a downward directed pressure-gradient force that acts against buoyant parcels. As one considers still coarser grid lengths, for example, 27 km, there is a continued narrowing of the vertical motion spectrum. Almost no downdrafts occur and the ascending motions are weaker in D2. Moreover, the mean vertical motion is much weaker in D2, only 1–2 cm s 21 versus 16 cm s 21 in CTRL. This latter fact accounts for the notably weaker storm produced in D2 as compared with CTRL. In light of the comparison of vertical motion spectra over a variation of model grid spacing of a factor of 9, we speculate that the bias in the area covered by upward motion is roughly proportional to the grid spacing. In the limit that an extremely coarse grid spacing were used (100–200 km grid spacing), the area used for averaging in our simulations would reduce to a single grid point, and, the spectrum of vertical motion would reduce to a single, positive value. However, the magnitude of the ascending motion appears to maximize for a grid spacing near the limit of validity of the hydrostatic approximation. At finer grid spacing, nonhydrostatic effects become important, limiting updraft strength. At coarser resolution two processes act to limit the strength of upward motion. First, the inverse dependence of vertical motion on length scale (for hydrostatic motions) implies that vertical motions should be weaker by a factor of 3 on a 27-km grid compared to a 9-km grid. Second, the weaker upward motion on a coarser grid gives the cumulus scheme more time to adjust the thermodynamic profile back to an equilibrium, subsaturated state. It is therefore more difficult to achieve grid-scale saturation on a 27-km grid than on a 9-km grid. With less grid-scale saturation, grid-scale overturning is relatively absent and strong upward motion does not occur. The presence of stronger downdrafts with finer grid spacing currently lacks a purely physical explanation. However, spectral broadening is nearly always the result of adding degrees of freedom to a nonlinear fluid system. These additional motions are possible with the introduction of a finer grid spacing in a system dominated by convective motions which seek the minimum resolvable scale. This statistical-dynamical fact, coupled with the bias present in the vertical velocity distribution at coarser grid spacing, virtually guarantees stronger downdrafts as resolution increases. 4. Storm track a. Initialization time In this section we consider three simulations initialized at 12-h intervals, 0000 UTC 7 September (I07), 1200 UTC 7 September (CTRL), and 0000 UTC 8 September (I08). Tracks for all three appear in Fig. 17.

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FIG. 17. Tracks for I07, CTRL, and I08 along with the observed storm track (Ls).

These show a steady improvement in the track prediction with later initialization time. We did not carry out an integration from 1200 UTC 8 September or later, though we anticipate that there would not be continued forecast improvement because most of the key features in the development (the upper-level trough and nascent surface cyclone) were offshore and not captured by the in situ observations. Initialization at 0000 UTC 7 September (I07) produces a storm which develops too far east and north. Development in I07 began around 1800 UTC 8 September, representing a lag of about 6 h relative to CTRL. Some hints of a secondary development in CTRL near the location of primary development in I07 are evident (not shown). This development occurs whether the simulations are run with 2 or 3 domains, so the fact that this erroneous development occurs near a nest boundary (see Fig. 1) in both I07 and CTRL is not significant. An important difference in the upper-tropospheric flow between I07 and CTRL is highlighted in Fig. 18. Note that dynamically balanced fields, computed on domain 1, are presented. The amplitude of the trough over Florida at 1200 UTC 8 September is weaker in I07. There is also a more extensive southwesterly jet in I07 over the region of cyclogenesis. These differences result from a poorer handling of the trough fracture in I07 compared to CTRL. Trough fractures have been studied in detail by Dean and Bosart (1996) wherein it was inferred that the process of trough fracture and cutoff low formation in the upper troposphere suffers from inherently poor predictability. Examination of the conditions at 850 hPa indicates some important differences in the low-level structure, particularly with respect to regions of warm advection, which accompany the greater extent of trough

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fracturing and greater southward penetration of the surface front in CTRL (Fig. 18). In I07, the low-level structure is more elongated along a southwest–northeast axis and the region of warm advection is located several hundred kilometers to the northeast of where it is in CTRL. The primary reason for this difference is stronger ridging throughout the troposphere over the eastern United States in CTRL at 1200 UTC 7 September (Fig. 19)2 . To the east of this ridging, a net northerly wind component pushes the cold front further south. The enhancement of northerly flow at 850 hPa, averaged from about 708 to 808W at 308N is 3–4 m s 21 , easily enough to account for the difference in the position of the baroclinic zone by 1200 UTC 8 September seen in Fig. 18. The upper tropospheric flow difference (CTRL 2 I07) near the elongated trough is dominated by anticyclonic shear. This appears to hasten the separation of the cutoff low from the primary trough to the north in CTRL. There is also a weak northerly flow difference which would help move the trough in CTRL further south and keep it in step with the lower-tropospheric frontal zone. In I07, the location of the first well-defined mesoscale cyclonic circulation near the surface coincides with the region of warm advection at 850 hPa (and 700 hPa, not shown). In DB, it was shown how mesoscale lifting (and attendant precipitation and latent heating) associated with warm advection and frontogenesis led to the production of lower-tropospheric PV anomalies, which, in turn, amalgamated into a nascent tropical storm. A similar evolution occurs here. The position of the region of low-level warm advection appears to determine the initial location of the mesoscale cyclogenesis. Because the location of lower-tropospheric warm advection is in error in I07, so is the location of tropical cyclogenesis. Our first attempt to simulate a storm beginning at 0000 UTC 8 September was entirely unsuccessful in that no storm formed. Inspection of the lower- to midtropospheric relative humidity field offshore revealed excessive dryness with humidities averaging only 50%– 60%. We modified the humidity field by replacing the relative humidity everywhere with the 12-h relative humidity forecast from CTRL. This was done on domain 1 only (81-km grid spacing). This new humidity field was interpolated to the higher-resolution domains and the simulation begun (I08). The offshore humidity at 700 mb was greater than 80% over a large area in the reconstructed analysis. The result with the improved humidity is striking. The development of the tropical cyclone proceeds similarly to that in CTRL, except that the track is much improved. There is virtually no trace of the spurious development over the northeastern portion of domain 3 2 The flow difference displayed in Fig. 19a is computed after removing the upper-tropospheric PV anomalies from both I07 and CTRL at 1200 UTC 7 September. The procedure is described in section 3a.

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FIG. 18. (a) Balanced geopotential heights and winds at 300 hPa from simulation I07 at 1200 UTC 8 Sep; (b) as in (a) but for simulation CTRL; (c) balanced temperature (dashed), geopotential (solid), and winds at 850 hPa from simulation I07 at 1200 UTC 8 Sep; (d) as in (c) but for simulation CTRL. Black dots indicate position of surface cyclone center deduced from maximum vorticity averaged over a 9 3 9 gridpoint box on domain 3 at the time shown in (c) and (d). The contour interval for geopotential heights is 20 m; for temperature it is 18C.

in I08. As apparent in Fig. 17, the storm in I08 tracks westward almost to the Florida coast near Cape Canaveral, stalls, then turns northward. The timing of the changes in storm motion follow closely the observations, particularly the cessation of westward motion, stalling, and commencement of northward motion. The improved track relative to CTRL allows precipitation to reach the northeast coast of Florida much as depicted by Fig. 12 from BB. The reason for the improved storm track in I08 relative to CTRL is primarily the differing behavior of the upper-tropospheric PV. In CTRL, the upper-level cyclonic circulation is elongated from southwest to northeast whereas in I08, it is more circular with more evidence of easterlies on the poleward flank of the positive PV anomaly (Fig. 20). In addition, the upper-level ridge to the east of the storm is somewhat weaker and further east in I08 and a stronger, mesoscale ridge is evident immediately poleward of the storm. Here we focus on 0300 UTC 9 September, the 27-h forecast from I08 and

the 39-h forecast from CTRL. At that time, the position of the two storms is nearly the same, but the motion of the CTRL storm is slowly northwestward and the motion of the storm in I08 is westward at about 6 m s 21 (Fig. 17). To isolate the contribution of upper-level PV anomalies to storm motion in each simulation, we calculate the total balanced flow in each case (on domain 1). Then we recompute a balanced flow with selected upper-level PV anomalies removed analogous to the technique used to compute initial conditions in the NOPV simulation (section 3a). The primary difference from the NOPV case is that the subdomain from which anomalies are extracted lies about 300 km further east than the subdomain used to initialize NOPV owing to the motion of the synoptic-scale features in the intervening time. We obtain four states of balanced geopotential and streamfunction. Only the streamfunction will be used to derive the steering winds and we denote the four streamfunction fields

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FIG. 19. (a) Relative vorticity from simulation I07 and difference in balanced, nondivergent (CTRL 2 I07) at 300 hPa for 1200 UTC 7 Sep (with upper-tropospheric PV anomalies removed,). Contour interval for vorticity is 5 3 10 25 s 21 with the zero contour dashed and negative values indicated with a thin, solid line. (b) Temperature from simulation I07 and difference in balanced, nondivergent (CTRL 2 I07) at 850 hPa for 1200 UTC 7 Sep. Contour interval for temperature is 3 K.

as c C , c*C , c I08 , and c*I08 , with capitalized portions of subscripts denoting the simulation and the asterisk denoting fields with the upper-level anomalies removed. The streamfunction field representing the difference in upper-level PV within the chosen subdomain is D c 5 c C 2 c*C 2 (c I08 2 c*I08 ).

(4.1)

We define upper-level PV anomalies to lie at 400 hPa and above. We average D c between 900 and 450 hPa to define the steering flow. It is not until 1200 UTC 8 September (24 h), as mesoscale cyclogenesis proceeds, that the concept of a steering flow appears relevant. Even then, the layer over which a reasonable match is found between vertically averaged wind and storm motion, roughly 900 to 450 hPa, is relatively shallow compared with what is often used for hurricane motion. This is probably a conse-

FIG. 20. PV and wind on 340 K surface for (a) CTRL and (b) I08 at 0300 UTC 9 Sep. PV values greater than 1 PVU are shaded; heavy solid line is PV 5 0 contour. Wind symbols are plotted at every fourth grid point.

quence of the relative shallowness of the PV anomalies in the core of the storm early in the development phase. The majority of the diabatically produced PV resides below 5 km, whereas at later times as the storm reaches hurricane intensity, the high PV extends to the upper troposphere and the motion appears to match winds averaged over a deeper column. We define storm motion at time t as the vector displacement of the center between t 2 1 h and t 1 1 h. The difference in storm motion at t 5 27 h (0300 UTC 9 September) between the CTRL and I08 can be represented by the vector (25.0, 21.5), or toward the west-

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FIG. 21. Difference in deep-layer streamfunction due to only the upper PV anomalies in I08 vs CTRL at 0300 UTC 9 Sep. Values have been scaled by 10 25 s m 21 to yield units of m (analogous to geopotential height). Contour interval is 5 m. The black dot indicates the location of the storm in CTRL at 0300 UTC 9 Sep, and the open circle indicates the position of the storm in I08 at the same time.

southwest at about 5.3 m s 21 . The difference represented by D c, interpolated to the location of each storm (the positions are nearly identical at 0300 UTC 9 September) results in a vector (25.6, 20.6) or toward the west at about 5.6 m s 21 . Thus, the difference in upper-level PV between CTRL and I08 within the subdomain accounts for nearly all the difference in the steering flow even though the PV anomalies included in the calculation reside entirely above the steering layer. The spatial pattern of D c is displayed in Fig. 21. It clearly shows an anticyclonic anomaly poleward of the storm and a cyclonic anomaly equatorward of the storm, yielding an easterly flow between the two. This pattern is consistent with a more ‘‘negative tilted’’ trough in simulation I08, which in turn, appears related to the initial amplitude of the southern portion of the trough fracture that occurred on 6–7 September. The later ini-

FIG. 22. Tracks for simulations with different cumulus schemes (CTRL omitted).

FIG. 23. PV and wind on 340 K from CTRL and BMJ1 1500 UTC 8 Sep (27 h). Plotting convention as in Fig. 20.

tialization allows a better representation of the fracture and the improved structure directly results in a better track prediction. This comparison points to the importance of capturing the detailed structure of synopticscale disturbances near the developing tropical cyclone. b. Cumulus scheme The storm track in BMJ1, GR, and EXP is more westward than in CTRL (Fig. 22). This results from the relative dominance of the explicit precipitation scheme in each of the sensitivity simulations BMJ1, GR, and EXP. It is well known that when grid-scale overturning occurs within the hydrostatic regime (5–10 km resolution or greater), the total, area-integrated upward mass flux is overestimated compared with simulations performed at cloud resolving resolution (Weisman et al. 1997). The reason is that (a) an entire 81 km 2 area will not likely overturn at once in reality, and (b) where convection does occur, nonhydrostatic effects limit the updraft strength within the convection. The overestimate of the mass flux has direct implications for the upperlevel potential vorticity, which, in turn, affects the ventilation flow and storm track. The PV on the 340 K surface at 1500 UTC 8 September from BMJ1 (representative also of GR and EXP) is shown in Fig. 23 along with the analogous field from

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PV which implies a superior treatment of precipitation and latent heating compared with CTRL. We have discounted this possibility in light of (a) physically unrealistic rainfall rates, and (b) the fact that I08 produced an excellent track with the same precipitation physics as in CTRL. The latter implies that the success of BMJ1 may be fortuitous and a case where errors in the initial condition are compensated by errors in physical representation. c. Other factors

FIG. 24. As in Fig. 21, but differences due to upper-level PV differences between BMJ1 and CTRL at 1500 UTC 8 Sep (27 h).

CTRL. The greater strength of both the cutoff low to the south and ridging to the north of the storm is apparent in BMJ1. The latter appears to result from greater overall mass flux in BMJ1, consistent with greater precipitation (Fig. 8) and stronger poleward outflow. The outflow displaces the tropopause upward and poleward, creating an anticyclonic PV anomaly. The greater strength of the cutoff low in BMJ1 is perhaps counterintuitive because one might expect that greater latent heating would result in more rapid weakening of cyclonic PV anomalies aloft. However, it appears from Fig. 23 that the enhanced convection in BMJ1 severs the physical link between the PV anomaly over Florida and that at higher latitudes sooner than in CTRL. This action appears to create a more circularly symmetric cutoff low in BMJ1 than in CTRL. We speculate that the more circular anomaly is more resistant to deformation in the ensuing 12-h period than is the more elongated anomaly in CTRL. Regarding the steering flow, we compute an analogous diagnostic to the one performed in section 4a to assess the difference in steering flow between CTRL and I08. Figure 24 shows D c valid at 1500 UTC 8 September (27 h, as shown in Fig. 23). The implied difference in steering velocity is about 7 m s 21 toward the southwest. Since the storm in CTRL is nearly stationary at 27 h, the motion of the storm in BMJ1 represents the difference in storm translation during the period 24–30 h, an average motion toward the westsouthwest at about 10 m s 21 . Thus, it is apparent that the differences in upper-level PV evolution once again are a key factor in storm motion. In the present case, changes in the precipitation physics result in changes in track through altering the upper-level PV and its associated ventilation flow. It is tempting to argue that BMJ1, because of its better track, had a more realistic treatment of the upper-level

Other factors contribute to the storm track to a lesser extent. For example, we performed simulations with the three-category microphysics scheme of Tao and Simpson (1993) and the simpler two-category scheme of Dudhia (1989). The maximum differences in storm position between either of these simulations and CTRL are less than half of the differences described in sections 4a and 4b. Variation of the PBL schemes, SST, and use of coarser and finer grid spacings produce still smaller differences in storm position. However, the relative insensitivity of the track to the inclusion of finer resolution may be underestimated due to the size of the innermost domain, limited by computational constraints. To fully assess the effect of finer resolution on track, the innermost domain should cover an area commensurate with the diabatically induced, synoptic-scale PV anomalies responsible for steering. This would require a domain of 500–1000 grid points on a side. Such simulations are feasible, but beyond the scope of this work. 5. Summary and conclusions The present study extends the results of DB by considering changes in the intensification and track brought about by changing initial conditions, boundary conditions, representation of physical processes, and grid spacing within MM5. Strong sensitivities are found for varying SST, initialization time, boundary layer physics, cumulus parameterization, and grid spacing on the innermost nest. The goal of this paper has been to understand the dynamics that govern the differences in the intensification and track of Tropical Cyclone Diana that were seen among the various simulations. The precursor upper-level disturbance is the catalyst for the tropical cyclogenesis. When we remove the upper-level trough and ridge from the initial condition, no storm forms. As the initialization time becomes later, the upper-level features become better defined and the simulation improves. When the model does not adequately forecast the upperlevel trough fracture, such that the resulting disturbance retains a southwest to northeast tilt, the cold front remains too far north and the upper trough is weaker and further north than observed. Warm advection along the front and the associated tropical cyclogenesis thus occur too far to the northeast.

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As the trough fracture becomes better resolved in the initial conditions, meaning more cyclonic PV breaks off from the main westerlies, the anticyclone poleward of the system is able to attain a greater amplitude. Between the anticyclonic anomaly poleward of the storm and the cyclonic anomaly on the equatorward side, the deeplayer easterlies drive the developing cyclone successively further west with later initialization time, improving the agreement with observations. The effect of the choice of cumulus parameterization on storm track can also be understood in terms of the effect on tropopause PV and the resulting changes in the deep-layer wind. In general, cumulus schemes that allow greater and more widespread explicit precipitation, associated upward mass flux, and divergent outflow aloft result in more westward storm tracks. Use of the Betts–Miller–Janjic, Grell and explicit-only schemes on the 9-km grid produce a more westward track compared with the Kain–Fritsch scheme. While the more westward track is in better agreement with observations, the track is more erratic using schemes that produced more gridresolved precipitation. The erratic behavior is due to the formation of numerous, intermittent, intense, mesoscale (almost grid-scale) vortices 100–200 km from the established center. Because this behavior resembles the type of problems discussed in Molinari and Dudek (1992) regarding grid-scale overturning at fairly coarse resolution, we suspect that the improved track with the Betts–Miller–Janjic and Grell schemes and with no cumulus scheme may be fortuitous. This is especially true in light of the fact that simply initializing 12 h later (0000 UTC 8 September) with the Kain–Fritsch scheme produces the best track of all the simulations. Simulations with three domains using the Kain– Fritsch scheme tend to intensify the storm too rapidly after the incipient vortex achieves tropical storm strength. The use of other cumulus schemes produce storms weaker than observed. The Betts–Miller–Janjic scheme is unable to inhibit deep convection governed by the explicit precipitation scheme, primarily due to its lack of downdrafts, which limit the potential buoyancy of boundary layer parcels. The Grell scheme, while including downdrafts, does not activate enough to suppress grid-scale overturning. The worst results with a 9-km grid spacing were obtained when the cumulus scheme is deactivated because the shortcomings seen in simulations using Grell and Betts–Miller–Janjic are simply magnified. The relative success of the Kain–Fritsch scheme is perhaps at odds with results from other studies wherein the best results are obtained using the Betts–Miller– Janjic scheme (Liu et al. 1997; Braun and Tao 2000). However, Braun and Tao simulate the genesis phase of Hurricane Bob using a 36-km grid. At that grid spacing, the assumptions used in deriving the Betts–Miller–Janjic scheme may be more appropriate. Liu et al. (1997) use a version of the Betts–Miller–Janjic scheme on an 18-km grid, but modify the trigger function to be more

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like the trigger for the Kain–Fritsch scheme, that is, they introduce an effective parcel buoyancy that is proportional to the large-scale vertical motion. In section 3d, it is argued that the widespread triggering of the Kain– Fritsch scheme is part of the reason that simulation CTRL treats the initial storm intensification fairly well; it reduces nonphysical grid-scale overturning on the 9km grid. When a fourth domain with a 3-km grid spacing is nested within domain 3 of simulation CTRL, the intensity prediction improves relative to that of CTRL. Comparing 9 km 3 9 km area averages from the 3-km and 9-km simulations, it is shown that the 3-km grid spacing produces notably more downdrafts and while some of the updrafts are also stronger, the overall spectrum of vertical motion is more symmetric about zero. The bias toward upward motion at coarser grid spacing is attributed to an improper treatment of nonhydrostatic effects. Weisman et al. (1997) show that this produces excessive upward mass flux, and in the present context, results in excessive vortex stretching and spinup of lower-tropospheric cyclonic circulation. One of the notable differences seen on the 3-km grid is the development of intense mesovortices just inside the radius of maximum wind. In many instances, these are strong enough to bring the tangential wind to zero locally. Vortices persist for roughly 3 h (about one revolution) and each is warm core. In some cases, the vortices are strong enough that their formation and subsequent absorption by the symmetric circulation cause a steplike trace in the time series of central pressure, with each step corresponding to one vortex life cycle. Other factors such as SST, PBL scheme, and analysis of moisture in the initial conditions are important in the intensification. These results are not surprising because such factors directly affect the amount of water vapor available for latent heat release and storm intensification. In general, results of varying the PBL physics agree with Braun and Tao (2000). Overall, we find that various choices of model ‘‘physics’’ can produce a storm of almost any intensity, ranging from a marginal tropical storm to a mature hurricane. It appears that a simulation more accurate than any discussed in this paper could be obtained by a judicious selection of grid spacing, initialization time, and model physical parameterizations, although this choice would not necessarily have either a physical justification or evince success in other cases. Furthermore, such an optimization would be predicated on a single forecast measure, and would likely change as one varies the measure of forecast accuracy. Based on our results, we caution against excessive tuning of model parameters to produce a single simulation used for diagnosing atmospheric phenomena. The more fundamental issue is investigating the nature of sensitivity, both physical and computational, that is apparent from altering aspects of the simulation. It appears that, at least in the present case, despite

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the difficulty in predicting the event, there are some deterministic aspects of the variations among different model configurations, such as effects of finer grid spacing and the behavior of cumulus and PBL schemes which may apply to other cases. However, the fact that such large sensitivities exist, despite the well-defined baroclinic precursor in this case, suggests that prediction of tropical cyclone formation and the subsequent track and intensification of the disturbance pushes the limits of predictability. Acknowledgments. The authors would like to thank Dr. Fuqing Zhang, Dr. Scott Braun and an anonymous reviewer for their helpful comments concerning the manuscript. Lance F. Bosart is funded under Grant NSF ATM-9612485. REFERENCES Arakawa, A., and W. H. Schubert, 1974: Interaction of a cumulus cloud ensemble with the large-scale environment, Part I. J. Atmos. Sci., 31, 674–701. Bao, J.-W., J. M. Wilczak, J. K. Choi, and L. A. Kantha, 2000: Numerical simulations of air–sea interaction under high wind conditions using a coupled model: A study of hurricane development. Mon. Wea. Rev., 128, 2190–2210. Betts, A. K., and M. J. Miller, 1993: The Betts–Miller scheme. The Representation of Cumulus Convection in Numerical Models, Meteor. Monogr., No. 46, K. A. Emanuel and D. J. Raymond, Eds., Amer. Meteor. Soc., 107–121. Bister, M., and K. A. Emanuel, 1997: The genesis of Hurricane Guillermo: TEXMEX analyses and a modeling study. Mon. Wea. Rev., 125, 2662–2882. Bosart, L. F., and J. A. Bartlo, 1991: Tropical storm formation in a baroclinic environment. Mon. Wea. Rev., 119, 1979–2013. Braun, S. A., and W.-K. Tao, 2000: Sensitivity of high-resolution simulations of Hurricane Bob (1991) to planetary boundary layer parameterizations. Mon. Wea. Rev., 128, 3941–3961. Burk, S. D., and W. T. Thompson, 1989: A vertically nested regional numerical prediction model with second-order closure physics. Mon. Wea. Rev., 117, 2305–2324. Burpee, R. W., and M. L. Black, 1989: Temporal and spatial variations of rainfall near the centers of two tropical cyclones. Mon. Wea. Rev., 117, 2204–2218. Davis, C. A., and K. A. Emanuel, 1991: Potential vorticity diagnostics of cyclogenesis. Mon. Wea. Rev., 119, 1929–1953. ——, and L. F. Bosart, 2001: Numerical simulations of the genesis of Hurricane Diana (1984). Part I: Control simulation. Mon. Wea. Rev., 129, 1859–1881. ——, E. D. Grell, and M. A. Shapiro, 1996: The balanced dynamical nature of a rapidly intensifying oceanic cyclone. Mon. Wea. Rev., 124, 3–26. Dean, D. B., and L. F. Bosart, 1996: Northern Hemisphere 500-hPa trough merger and fracture: A climatology and case study. Mon. Wea. Rev., 124, 2644–2671. DeMaria, M., 1996: The effect of vertical shear on tropical cyclone intensity change. J. Atmos. Sci., 53, 2076–2087. Dengler, K., and M. J. Reeder, 1997: The effects of convection and baroclinicity on the motion of tropical-cyclone-like vortices. Quart. J. Roy. Meteor. Soc., 123, 699–725. Dudhia, J., 1989: Numerical study of convection observed during the winter monsoon experiment using a mesoscale two-dimensional model. J. Atmos. Sci., 46, 3077–3107. Emanuel, K. A., 1986: An air–sea interaction theory for tropical cyclones. Part I: Steady state maintenance. J. Atmos. Sci., 43, 585–604.

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