1100 MONTHLY WEATHER REVIEW VOLUME 130

Numerical Simulations of the Genesis of (1984). Part II: Sensitivity of Track and Intensity Prediction

CHRISTOPHER DAVIS National Center for Atmospheric Research,* Boulder, Colorado

LANCE F. B OSART University at Albany, State University of , Albany, New York

(Manuscript received 14 June 2001, in ®nal form 6 November 2001)

ABSTRACT The authors examine numerous simulations that probe the dynamics governing the intensi®cation and track of Tropical 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, , and grid spacing. Simulations with cumulus schemes that allow more grid-scale precipitation on the 9-km grid exhibit unrealistic grid-scale over- turning and slower intensi®cation, 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 intensi®cation 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 intensi®cation with a 9-km grid spacing. Manual analysis of surface data produces a sea surface temperature (SST) ®eld 1Њ±2ЊC 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 out¯ow aloft. The out¯ow 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 ¯ow 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-de®ned 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 cyclone along a quasi-stationary front that had pene- trated to remarkably low latitudes for early September. a. Review of Part I A cold-core upper-tropospheric trough is important for The development of Hurricane Diana (1984) is no- initiating baroclinic development, the precursor of trop- table for the important role of synoptic-scale, baroclinic ical cyclogenesis. precursors. As shown in Bosart and Bartlo (1991, here- The modeling study of Davis and Bosart (2001, here- after BB), the storm begins as a subtropical baroclinic after DB) captures the transformation of the baroclinic disturbance into a warm-core mesoscale vortex within the Pennsylvania State University±National Center for * The National Center for Atmospheric Research is sponsored by Atmospheric Research ®fth-generation Mesoscale Mod- the National Science Foundation. el (MM5). In the simulation, weak baroclinic devel- opment begins as a cold-core upper-tropospheric trough Corresponding author address: Christopher A. Davis, National moves off the coast. Low-level warm advection, Center for Atmospheric Research, P.O.Box 3000, Boulder, CO 80307. induced mainly by the upper-level disturbance initiates E-mail: [email protected] widespread precipitation and latent heating poleward of

᭧ 2002 American Meteorological Society

Unauthenticated | Downloaded 09/24/21 09:07 PM UTC MAY 2002 DAVIS AND BOSART 1101 a quasi-stationary surface front. The heating produces mental shear (e.g., Gray 1982; DeMaria 1996), the me- numerous low-level positive potential vorticity (PV) soscale distribution of precipitation (e.g., Krishnamurti anomalies. A dominant PV anomaly forms near the up- et al. 1998), presence of concentric eyewalls (e.g., Wil- shear (western) extremity of the lower-tropospheric loughby et al. 1982), dissipative heating in the core frontal zone, ampli®ed further through latent heating. (Bister and Emanuel 1997; Zhang and Altshuler 1999), The incipient vortex sweeps surrounding PV anomalies angular momentum ¯uxes resulting from interactions around itself, growing further by eddy vorticity ¯uxes with midlatitude upper-level troughs (e.g., Riehl 1954; as the anomalies are axisymmetrized. The transition to Molinari et al. 1998), and storm-induced sea surface warm core occurs in about 8 h, from 1000 UTC 8 Sep- temperature changes (e.g., Schade and Emanuel 1999). tember to 1800 UTC 8 September. A 12-h period of In addition, numerical simulations show considerable quiescence follows during which the boundary layer and sensitivity to a number of factors that are entirely spe- lower troposphere near the storm moisten. Renewed ci®c to models themselves as contrasted with the above deepening in response to enhanced ¯uxes of water vapor factors, which are all believed to be true sensitivities in from the ocean then occurs and the simulated storm nature. A key sensitivity is horizontal grid spacing. No- reaches hurricane intensity by 1800 UTC 9 September. table improvement of intensity prediction occurs as the In the present paper, we examine the robustness of grid spacing decreases to roughly the radius of maxi- the mechanism advanced in DB of the transformation mum wind (RMW) or less (Walsh and Watterson 1997). of the baroclinic disturbance into Tropical Storm Diana Further sensitivity has been reported as the grid spacing and eventually into Hurricane Diana. Dynamics of the is reduced below 10 km, such that simulations with initial development, featuring warm-core transforma- resolutions of about 5 km are able to capture eyewall tion, are examined using different treatments of physical dynamics and better resolve storm out¯ow (Tripoli processes (cloud physics, cumulus parameterization), 1992; Liu et al. 1997; LeMarshall and Leslie 1999; variations in horizontal grid spacing (27 km, 9 km, and Braun and Tao 2000). 3 km), different sea surface temperature (SST) analyses, The effect of varying model grid spacing and physical and different initial conditions. Furthermore, we inves- parameterizations in ®ner-scale simulations (Ͻ10 km tigate the effect of these variations on the intensi®cation grid spacing) of formation has not been of the storm to hurricane strength and on the track of investigated extensively. Based on simulations of me- Tropical Cyclone Diana. We will use the behavior of soscale convective systems, we expect considerable sen- simulations with perturbed physical parameterizations, sitivity of tropical cyclone genesis to changes in grid initial conditions, and SST, and the extensive body of spacing between roughly 2 and 20 km (Molinari and existing knowledge regarding sensitivities in numerical Dudek 1992) due to the lack of appropriate separation simulations of tropical to obtain a more com- between resolved and parameterized scales of motion. plete understanding of the essential processes involved In many simulations, an initial vortex is imposed, pre- in the development of Diana. cluding any chance of simulating the earliest stages of and investigating the dynamics of the process and the related sensitivities, both natural and b. Review of known sensitivities in numerical numerical. Much of the motivation for the present paper simulations is to address this issue. 1) INTENSIFICATION 2) TRACK A large body of research focuses on the sensitivity of the numerical treatment of air±sea heat and water In recent years there have been numerous extensions vapor exchange in mature hurricanes. Based on work of the basic concept of tropical cyclone motion resulting by Emanuel (1995, 1999) the intensi®cation rate of hur- from beta gyres, the circulation around tropospheric PV ricanes seems to depend on thermodynamic properties anomalies arising from meridional advection of plane- of the large-scale environment and the details of the air± tary vorticity. More generally, it is recognized that any sea exchange under the core of the storm. In particular, azimuthal wavenumber one asymmetry in PV gives rise a key parameter is the ratio of the exchange coef®cients to a ventilation ¯ow, which can effectively steer the of enthalpy and momentum; the larger this ratio, the tropical cyclone. In general, the largest gradients of PV faster the storm can intensify. Comparing simulations are located at the tropopause and therefore, perturbation of (1991) using four different planetary of these gradients can yield important ¯ow anomalies. boundary layer (PBL) schemes and ®ve permutations Studies by Wu and Emanuel (1993, 1995a,b) demon- thereof (a total of nine simulations), Braun and Tao strate how, by virtue of the large horizontal scale of the (2000) show that the intensi®cation rate is roughly pro- upper-level anticyclone, the circulation associated with portional to this ratio calculated from each PBL for- this perturbation can penetrate through the troposphere mulation. and affect a deep layer. This anticyclone is partly due Many other factors are suggested as being important to the explicit material reduction in PV above the max- in the intensi®cation of hurricanes, including environ- imum heating and, perhaps more importantly, due to the

Unauthenticated | Downloaded 09/24/21 09:07 PM UTC 1102 MONTHLY WEATHER REVIEW VOLUME 130 rearrangement of tropopause PV due to the storm out- Two additional PBL schemes are used, the Burk± ¯ow. The notion of beta gyres and tropopause-based Thompson (1989) scheme and the Blackadar scheme asymmetries acting together appears in Wang and Hol- (Zhang and Anthes 1982). The Blackadar scheme is a land (1996a,b). ®rst-order closure scheme very similar in concept to the As demonstrated by Shapiro and Franklin (1999), it MRF scheme. We include it here because Braun and is about as common for asymmetries within 1500 km Tao (2000) demonstrated greater vertical mixing and a of the storm center to govern its track as it is for anom- deeper boundary layer in the MRF scheme. The treat- alies outside 2000 km radius to be dominant. In the ment of surface ¯uxes in the two schemes is nearly former category, the asymmetries responsible for steer- identical. The Burk±Thompson scheme predicts turbu- ing are probably more strongly in¯uenced by the storm lent kinetic energy and employs a different surface layer itself, particularly the diabatic effects at high levels. As scheme than used in the MRF scheme (Braun and Tao suggested by Dengler and Reeder (1997) and Henderson 2000). The reader is referred to Braun and Tao (2000) et al. (1999), the ability of numerical models to correctly for a more detailed comparison of the formulations of simulate the out¯ow from a tropical cyclone bears di- the PBL schemes. rectly on the upper-level asymmetries produced and The sea surface temperature analysis in CTRL is a hence on the ventilation ¯ow. Henderson et al. (1999) blend of a manual analysis over the region of cyclo- suggest that part of the de®ciency stems from inaccurate genesis (essentially over domain 3) with the operational initial conditions. However, we will show that the un- navy SST analysis on coarser domains. The manual certainties related to the parameterization of convective analysis methodology is outlined in section 3b and also processes can have as large an effect on storm track as in DB. A sensitivity study using only the navy SST uncertainties in initial conditions. (NAVSST) analysis is also performed. Table 1 summarizes the various sensitivity simula- tions considered in this paper. In all cases, two-way 2. Model description nesting is employed and initial conditions on nests are The modeling system used here is the PSU±NCAR obtained from interpolation from the coarsest domain. model [MM5, Version 2; Grell et al. (1994)]. The do- Simulation CTRL was the focus of DB. For this sim- main con®guration (Fig. 1) of the model is described ulation, we integrated three domains, with an innermost in DB. The control simulation (CTRL) uses the medium- grid spacing of 9 km, all beginning at 1200 UTC 7 range forecast model (MRF) planetary boundary layer September 1984. scheme (Hong and Pan 1996), the numerical weather prediction explicit microphysics scheme (NEM; Schultz 3. Intensi®cation 1995), the Dudhia (1989) radiation scheme, and the Kain±Fritsch cumulus scheme (Kain and Fritsch 1993). Figure 2 shows a set of time series of central sea level For some simulations in the present study, a fourth do- pressure for most of the simulations to be discussed in main is added (section 3e) wherein no implicit scheme this section. The large spread about the observed deep- is used. ening rate indicates the dramatic effect that variations Numerous physics options are examined in the pre- in model physics, initial and boundary conditions can sent paper in addition to the combination present in have. Later, we examine the reasons for the behavior of simulation CTRL. Because there is evidence for sen- the simulations shown in Fig. 2. sitivity of tropical cyclone prediction to a number of physical processesÐfor example, cumulus parameteri- a. Modi®ed upper-level PV zation (Puri and Miller 1990), microphysics (Lord et al. 1984), and boundary layer processes (Braun and Tao In DB, it was found that the upper-level trough-ridge 2000)Ðit is important to investigate the use of schemes couplet was important for focusing the vertical motion with fundamentally different formulations. and latent heating that allowed the initial spinup of Di- For implicit precipitation, we use the Betts±Miller± ana. Here we quantify the effect of the upper-tropo- Janjic (Betts and Miller 1993) and Grell (1993) schemes. spheric anomalies by removing them from the initial The former is a convective adjustment scheme wherein state and then integrating the forecast as before. the reference equilibrium pro®le can be varied (see sec- Removal of a portion of the upper-level wind and tion 3d). The Grell (1993) scheme is an adaptation of temperature features is performed using a PV inversion the Arakawa±Schubert (1974) scheme with downdrafts technique (Davis and Emanuel 1991; Davis et al. 1996), added. Alternative explicit precipitation schemes in- wherein the nonlinear balance condition is imposed. The clude the Tao and Simpson (1993) scheme, a three- inversion is done on domain 1. We de®ne a volume that category scheme (rain, snow, and hail) that has been encompasses the anomalous PV associated with the cold applied extensively to tropical convection, and the so- trough and downstream ridge in the upper troposphere called simple ice scheme (Dudhia 1989), which treats (Fig. 3). The east and west boundaries of the region hydrometeors as rain at temperatures above freezing and approximately span one zonal ``wavelength'' of the up- as snow at temperatures below freezing. per-level disturbance (about 2500 km). The northern

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FIG. 1. Domain con®guration, including stationary location of domain 4 (3-km grid spacing, 151 ϫ 151 points). The gray box de®nes the area from which anomalies of potential vorticity are de®ned.

boundary is chosen within the thinnest portion of the area are (i1, i 2) and (j1, j 2), respectively, with a center narrow positive PV anomaly that connects the strato- at (ic, jc). The PV averaged on (j1, j 2) for each i is spheric reservoir of high PV with the cold-core low to denoted Qi. The modi®ed PV coincides with the original the south. The southern boundary is chosen to lie several PV at the east and west end points of the averaging area hundred kilometers south of the anomalously large PV and linearly transitions to the ``zonally'' averaged PV within the trough. The bottom of the volume is 600 hPa at the center. and the top is 150 hPa. This layer is chosen to encom- To perform the inversion, we adopt Neumann upper pass the deformed tropopause. Similar results are ob- and lower boundary conditions for the streamfunction tained if the bottom of the layer is as high as 400 hPa. and geopotential ®elds and specify the potential tem- On each pressure level, the PV at each i (the north± perature to be equal to the potential temperature of the south grid index) is averaged zonally over grid indices initial condition of CTRL at 975 hPa and at 125 hPa, j on the interval (j1, j2). The PV in this interval is re- the lower and upper boundaries of the inversion domain, placed by a new PV ®eld de®ned as respectively. On lateral boundaries of domain 1, we specify geopotential and streamfunction equal to their j Ϫ jj11Ϫ j values in the initial state of CTRL. The wind within the qi,jϭ q i,j1 1 ϪϩQ i ΂΃jc Ϫ jj1 c Ϫ j1 lowest 50 hPa in the perturbed initial condition is ob- tained by applying the same average fractional speed when ( j Յ jc) and (3.1a) reduction and the same average angular rotation of the wind that was present in the control simulation initial j Ϫ jjccϪ j state (DB). That is, if the average rotation over the low- qi,jϭ q i,j2 1 ϪϩQ i ΂΃j2 Ϫ jjc 2 Ϫ jc est 50 hPa is 30Њ and speed reduction is 20% in CTRL, we apply these same corrections to the velocity in the when ( j j ). (3.1b) Ͼ c perturbed initial condition. Here, i and j are the indices for the ``north±south'' and From Figs. 3a and 3b, the difference between initial ``east±west'' directions, respectively, consistent with the conditions of the no-trough (NOPV) simulation and order of indices in MM5. The bounds on the averaging CTRL at upper levels is obvious. The cutoff low over

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TABLE 1. List of simulations.

Simulation Min⌬x Initial conditions PBL±SFC Cumulus CTRL 9km 12Z 7 Sep MRF Kain±Fritsch NOPV 9km 12Z 7 Sep (no trough) MRF Kain±Fritsch NAVSST 9km 12Z 7 Sep MRF (navy SST) Kain±Fritsch BMJ1 9km 12Z 7 Sep MRF Betts±Miller±Janjic (ML) BMJ2 9km 12Z 7 Sep MRF Betts±Miller±Janjic (Trop) GR 9km 12Z 7 Sep MRF Grell EXP 9km 12Z 7 Sep MRF none (D-3 only) BT 9km 12Z 7 Sep Burk±Thompson Kain±Fritsch BKD 9km 12Z 7 Sep Blackadar Kain±Fritsch BKD±BMJ 9km 12Z 7 Sep Blackadar Betts±Miller±Janjic (ML) 2D 27 km 12Z 7 Sep MRF Kain±Fritsch 4D21 3 km (at 21 h) 12Z 7 Sep MRF none (D-4 only) 4D24 3 km (at 24 h) 12Z 7 Sep MRF none (D-4 only) 4DI08 3 km (at 12 h) 12Z 7 Sep MRF none (D-4 only) I07 9km 00Z 7 Sep MRF Kain±Fritsch I08 9km 00Z 8 Sep MRF Kain±Fritsch

Florida in CTRL does not appear in the initial conditions The navy SST analysis does not capture the narrow of NOPV. In the lower troposphere, in addition to weak- tongue of warm SSTs extending northward to the east er cyclonic circulation implied by the sea level pressure of Florida that is apparent in Fig. 1 of DB. The sea state ®eld in NOPV, the warm advection region to the east preceding the development of Diana was probably high- of Florida is nearly eliminated (not shown). In NOPV, ly disturbed owing to the steady northeasterly surface there is little to focus the vertical motion within the winds of about 15 m sϪ1 present in the area where many baroclinic zone. ship and buoy observations were taken. Hence, it is not Examination of the 36-h forecast in each simulation likely that the difference between navy and analyzed (Figs. 4a and 4b) reveals that the weak inverted trough SST is due to the presence of a shallow layer of warmer present initially in NOPV migrates westward to the Gulf water residing on the surface, as can occur in relatively of Mexico over 36 h, but does not develop a notable calm conditions. The difference could be due to the surface signature, whereas there is a well-de®ned storm in¯uence of climatological information and the coarse- in CTRL that had reached tropical storm strength. Note ness of the navy analysis. that in NOPV, the water vapor mixing ratio is unaltered The cooler SSTs in NAVSST result in a signi®cantly compared to CTRL. Hence, since the low-level tem- weaker development as compared to CTRL such that perature is also the same, the thermodynamic stability by 60 h, the central pressure in NAVSST is 27 hPa of the atmosphere is very similar to that in CTRL.1 higher than in CTRL. The evolution of the NAVSST Indeed, convection occurs in NOPV, but it is not or- simulation is broadly similar to CTRL in terms of the ganized and localized to the extent seen in CTRL. Our timing of development and the overall track. As can be interpretation is that the low-level inverted trough is not seen from Fig. 5, beginning near 33 h, the end of the a suf®ciently strong disturbance to organize convection ®rst deepening phase, there is a high correlation between on its own, so the system does not amplify. the ␪e difference at the storm center, expressed as a b. SST As described in DB, hand analyses supplement the navy's operational SST ®eld over the region of cyclo- genesis (see Fig. 1 of DB). Because of the subjectivity of the analysis, it is reasonable to investigate the sen- sitivity to using this analysis as compared with the un- supplemented navy analysis. The navy SSTs under the storm are almost uniformly 1Њ±2ЊC 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 con- vective available potential energy (CAPE). However, it appears that differences in CAPE between CTRL and NOPV are small in the FIG. 2. Minimum sea level pressure time series for simulation present case, and differences are particularly small between the upper- CTRL and selected sensitivity simulations. Observations are indicated level trough and ridge where much of the convection occurs. with ®lled 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 ϭ 10Ϫ6 m2 Ϫ1 Ϫ1 Kkg s ) and darker shading indicates PV greater than 4 PVU. FIG. 4. Near-surface winds (40 m MSL) and 3-h accumulated pre- cipitation valid at 36 h (0000 UTC 9 Sep) for (a) NOPV and (b) CTRL. theoretical pressure de®cit ⌬p(hPa) ϭ 2.5⌬␪e(K), (Malkus and Riehl 1960) and the simulated sea level central pressure difference. One expects this result for storm-induced surface stresses weakens the hurricane in mature hurricanes (Malkus and Riehl 1960; Emanuel proportion to the cooling of the ocean under the core 1986), but here, the correlation exists for a storm of (Bao et al. 2000; Shay et al. 2000). The amount of modest intensity. cooling varies inversely as the depth of the thermocline In the version of MM5 used herein, SST does not and the translational speed of the storm. Application of vary in time, therefore, the effects of oceanic responses a coupled model is beyond the scope of the present to atmospheric forcing on storm intensity cannot be ex- study, however, given the relatively slow movement of amined. Coupled atmosphere±ocean modeling studies Diana, we can speculate that inclusion of the upwelling of hurricanes generally show that upwelling caused by effect would reduce the intensity of the simulated

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by which the ¯uxes are distributed vertically, it is im- portant to examine the sensitivity of the simulations to different PBL schemes or variations of parameters with- in 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 inten- si®cation is also very similar to that in CTRL. Consis- tent with these results, Braun and Tao (2000) also ®nd FIG. 5. Time series of central sea level pressure difference that the Burk±Thompson scheme produces a storm of (NAVSST Ϫ CTRL) between CTRL and NAVSST (heavy solid line), greater intensity than either the MRF or Blackadar an estimate of this difference using the central ␪e difference (thin solid line), and the SST difference (CTRL Ϫ NAVSST; dashed). 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 storms. Given the disturbed sea state that preceded de- strength (Fig. 6). Ultimately, the azimuthally averaged velopment, and the fact that the warm SSTs were within surface humidity falls below 70% outside a radius of the where they were not likely associated 100 km (Fig. 6d). The Burk±Thompson scheme main- with shallow, warm water susceptible to cooling fol- tains the humidity at outer radii at about 85%, a seem- lowing an increase in surface winds, it is possible that ingly more reasonable value (Fig. 6c). The Blackadar the reduction of intensity would be modest. schemes yields near-surface humidities that are similar to those produced by the Burk±Thompson scheme, av- c. PBL schemes eraging 80% to 85% at radii greater than 100 km (not shown). Because the ¯uxes of water vapor from the ocean are During the genesis phase, however, the differences the critical source of energy for the developing hurri- between the schemes are in the same sense, but smaller cane, and because the PBL scheme is the primary means (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 ob- Thompson scheme and only about 0.7 in the MRF and servations of dewpoint depression (taken from BB, their Blackadar schemes. Emanuel (1995) shows that the ul-

Fig. 9) are composited over a 12-h period in a storm- timate storm intensity should depend on the ratio CK/ relative coordinate system (Fig. 7). Three times are in- CD. Thus, it appears that there are two factors contrib- cluded: 1200 and 1800 UTC 8 September and 0000 UTC uting to enhanced development in BT: (1) the shallower 9 September. Coastal observations are used at 0000 UTC and moister PBL, arising from less vertical mixing than 9 September when Diana was approaching Cape Ca- in the MRF scheme, which implies that a given ¯ux of naveral, but inland observations are not used. No ob- water vapor can more easily increase ␪e in the boundary vious trend versus time or radius is apparent in Fig. 7 (Table 2). Two observations occurred within , but generally, the dewpoint depression is 2Њ±4ЊC, cor- TABLE 2. Observations of humidity vs radius from storm center. responding to a relative humidity range of approxi- Here, ␴ is the standard deviation of dewpoint depression within each mately 85% to 80%, respectively (Table 2). This range 50-km radius bin. is between the humidities in CTRL (70%±75%) and BT r (km) Td (ЊC) RH (%) ␴ (ЊC) (about 90%), and close to the near-surface humidity 0±50 2.7 85 0.8 found in BKD (not shown). 50±100 2.5 86 1.6 Braun and Tao (2000) also note that in addition to 100±150 3.2 83 0.5 having a more moist PBL than the MRF scheme, the 150±200 3.8 80 0.9 ratio of moist enthalpy ¯ux coef®cient (C ) to the fric- 200±250 3.2 83 1.3 K 250±300 3.4 82 1.4 tional drag coef®cient (CD) is about unity in the Burk±

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layer, and (2) the greater value of CK/CD than in either the Blackadar or MRF schemes, which implies a greater amount of latent energy available for intensi®cation rel- ative 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 in¯uence on the intensity than the mix- ing within the PBL. d. Cumulus schemes The use of an implicit precipitation scheme on the 9- km grid may be regarded as questionable from a phys- ical point of view (Molinari and Dudek 1992). In this FIG. 8. Hourly rainfall, averaged over a 153 ϫ 153 km2 area cen- section, we examine simulations with the Betts±Miller± tered on the storm for BMJ and CTRL, expressed as mm (grid Janjic (Betts and Miller 1993) and Grell (Grell 1993) point)Ϫ1. The heavy solid curve represents explicit precipitation from schemes, and also examine a simulation in which the CTRL (CTRLexp); the heavy dashed curve is explicit precipitation from BMJ1 (BMJ ); thin lines denote implicit precipitation, solid implicit scheme withheld on the 9-km grid. exp for CTRL (CTRLcp), dashed for BMJ (BMJcp). Curves for CTRL A commonly used scheme in the Tropics is the Betts± begin later due to dif®culties in locating center prior to 16 h (0400 Miller scheme (Betts and Miller 1993), especially for UTC 8 Sep). 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 (here- eters are in excess of 100 mm. This rate is conceivable after BMJ). This scheme is a convective adjustment for individual convective cells, but because entire me- scheme rather than a model of cloud evolution as is the soscale regions experience this rainfall in the simulation, Kain±Fritsch scheme. Thus, it is simpler and much of the validity of the rainfall prediction is highly ques- the sensitivity involves the choice of reference pro®le tionable (Venugopal et al. 1999). toward which the atmosphere is adjusted and the time- In BMJ1, the intensity of the storm is reduced relative scale over which adjustment occurs. The primary pa- to CTRL and the storm is weaker than observed (Fig. rameters to be adjusted are saturation pressure de®cits 2). During the early development of the storm (prior to for air near cloud base, the freezing level, and near the 1800 UTC 8 September), the rainfall rates are signi®- tropopause along with a parameter that controls how cantly larger in BMJ1 (Fig. 8). The peak rainfall rate closely the reference pro®le follows a moist adiabat. occurs in BMJ1 between 0600 and 1200 UTC 8 Sep- The pressure de®cit is the change in pressure required tember and was about 1.7 times the maximum rainfall to bring a parcel to saturation. Typically, for tropical rate in CTRL. The majority of the rainfall during these applications, the stability parameter is nearly unity, enhanced periods is produced by the explicit precipi- meaning that the reference pro®le exhibits a moist adi- tation scheme. The rainfall due to the implicit scheme abatic lapse rate. is approximately 1 mm hϪ1 (averaged over the 17 ϫ 17 We use two sets of pro®les, one perhaps more rep- gridpoint box, or about 23 000 km2). resentative of midlatitudes, the other more representa- The apparent contradiction between the much heavier tive of the deep Tropics. The former is de®ned by the rain rates and the weaker development in BMJ1 relative to CTRL can be explained by considering the spatial pressure de®cits (␦pB, ␦p 0, ␦pT) ϭ (Ϫ38.75, Ϫ58.75, Ϫ18.75) in hPa with a stability parameter of 0.9. Sub- distribution of precipitation and associated vorticity and scripts B, 0, and T refer to cloud base, freezing level, potential vorticity anomaly generation relative to the and tropopause, respectively. The tropical pro®le de- storm center. Although the precipitation in BMJ1 from rives from Betts and Miller (1993); (␦pB, ␦p 0, ␦pT) ϭ 21±27 h (0900 to 1500 UTC 8 September) is heavier (Ϫ20.0, Ϫ40.0, Ϫ20.0) in hPa with a stability parameter than in CTRL, it is distributed in an elongated strip of 1.0. As the present case is a hybrid tropical±extra- along a southwest±northeast axis and the resulting 900 tropical development, it is not clear a priori which set hPa PV shows a similar distribution (Fig. 9). Over the of parameters is more appropriate. next 6 h, the precipitation and PV ®elds in BMJ1 show The simulation with ``midlatitude'' parameters less linear structure (Fig. 9c), but there is still a tendency (BMJ1) produces the better storm intensity and track for heavy precipitation and strong anomalies further but the tropical parameters (BMJ2) produce what ap- from the storm center than in CTRL (Fig. 9d). In sim- peared to be more plausible rainfall rates (roughly half ulation CTRL, most of the precipitation at large radii of the rates in simulation with midlatitude parameters). is produced by the Kain±Fritsch scheme (not shown). Since rainfall is not measured, this is partly conjecture. Because the implicit precipitation is generally light, its Peak hourly rainfall amounts with midlatitude param- 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 ®elds than the effect of the locally the mean tangential circulation when they are axisym- heavy explicit precipitation in BMJ1. metrized. Numerous studies on the intensi®cation of vortices The effect of vorticity anomalies at various radii can from diabatic heating (e.g., Schubert and Hack 1982) be quanti®ed using similar vorticity ¯ux diagnostics as show that heating at large radii reduces spinup ef®- were shown in DB (their Fig. 14). Brie¯y, the change ciency. In addition, work by Montgomery and Enagonio in azimuthally averaged, tangential wind is caused (1998) further supports the concept of a critical radius mainly by two contributions, the vorticity ¯ux due to beyond which cyclonic PV anomalies do not intensify the symmetric radial circulation,u ␩ and the eddy ¯ux

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®rst 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 or- ganization 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 FIG. 10. Radial pro®les of eddy-induced angular momentum chang- if there is grid-resolved upward motion at the lifted es from CTRL (heavy solid) and BMJ1 (dashed). All quantities rep- resent averages from 21 to 36 h and from roughly 0 to 2 km MSL. condensation level (Fritsch and Kain 1993). Other schemes simply check for buoyancy by lifting parcels representative of individual layers. Given widespread uЈ␨Ј. Here u is the radial wind, ␩ is the absolute vor- upward motion induced by frontal ascent and the initial ticity, and ␨ is the relative vorticity. Overbars and primes presence of minimal convective inhibition, the Kain± denote the azimuthal average and deviations from it, Fritsch scheme becomes widely active. The Kain± respectively. Here, we highlight the differences due to Fritsch scheme is effective in stabilizing the lower tro- the eddy contribution. To more consistently compare posphere to parcel ascent, but maintains marginal con- accelerations at different radii, we examine the the ditional instability for lifted layers. We believe this is t, where ␷ is the why the explicit precipitation is con®ned to the frontץ/ ␷ץchange in angular momentum, r tangential wind. The curves in Fig. 10 illustrate that the and, later, the eyewall in CTRL, where strong mesoscale eddy-induced accelerations are weaker and displaced to lifting persists. The formation of lower-tropospheric greater radii in BMJ1 than in CTRL. In particular, the vorticity anomalies is similarly con®ned to regions contribution from eddy ¯uxes in BMJ1 is larger for r where the anomalies already exist, and ampli®cation Ͼ 200 km. It appears that an important contribution to occurs more readily. In the other simulations, the cu- the smaller intensi®cation rate in BMJ1 relative to mulus scheme is not active enough to adjust the tro- CTRL is the production of PV anomalies and an as- posphere given the continued destabilization due to me- sociated increase of tangential wind at larger radii than soscale lifting and input of latent energy from the ocean in CTRL. beneath. The result is a less con®ned distribution of grid- In performing simulation BMJ2 we attempt to correct scale precipitation and latent heating. Multiple vorticity for the excessive precipitation rates in BMJ1 by using anomalies form on marginally resolved scales, separated a thermodynamic pro®le with less potential instability. by distances too great for merger on the timescale of The result is more plausible rainfall, but a storm of only the simulation. half the intensity as in BMJ1 (not shown), even further from what is observed. e. Grid spacing We perform three other simulations, one with the Grell (1993) scheme (GR) and another with no cumulus One of the more notable sensitivities in our simula- scheme (EXP). A third simulation uses the Blackadar tions is that of variations in horizontal grid spacing and PBL scheme and the Betts±Miller-Janjic cumulus the associated change in physical processes. We con- scheme (BKD±BMJ1). All three simulations produce sider both coarser grid spacing (27 km) and ®ner grid notably weaker development than CTRL or BMJ1. The spacing (3 km), the latter requiring a restricted (and evolution in GR and EXP is qualitatively similar. The sometimes translating) domain because of computation- dominance of the explicit scheme in each (by de®nition al constraints. At 3-km grid spacing we forgo an implicit in EXP) produces excessive local perturbations to the cloud scheme. pressure and wind ®elds near each major grid-scale overturning. Similar behavior is noted in many previous 1) 27-KM GRID SPACING studies where the explicit precipitation scheme assumed a dominant role at coarse resolution (Kuo et al. 1996). In the simulation with a grid spacing of 27 km (de- It appears that 9-km grid spacing is too coarse to forgo noted 2D), we retain the same physical parameteriza- an implicit scheme in this case. tions as in CTRL. Arguably, the parameterizations (e.g., Simulation BKD±BMJ1 produces only a weak, syn- Kain±Fritsch) are more appropriate at this grid spacing. optic-scale cyclone. Localized heavy rainfall, governed In simulation 2D, the storm is considerably weaker than by the explicit precipitation scheme, occurs within the CTRL and also the observed storm (Fig. 2). We believe

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domain, along with simulation CTRL and the obser- vations 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) ap- pears 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 ®ne enough to properly treat the tropical convection, at least not until mesoscale vertical motion becomes more well organized after an initial cyclogenesis period. FIG. 11. Minimum sea level pressure for CTRL and the three simulations using a fourth domain. In the remainder of the section, we focus on simu- lation CTRL-4D21 and contrast it with CTRL. From Fig. 12, it can be seen that the three-domain simulation that this de®ciency stems from a lack of grid-scale sat- produces a fairly symmetric vortex (Figs. 12a and 12c) uration within the frontal zone and the associated gen- whose maximum winds at 900 hPa are about 42 m sϪ1, eration of mesoscale PV anomalies in the lower tro- contrasted with a maximum speed in CTRL-4D21 of 30 posphere. Thus, the initial spinup of a mesoscale vortex msϪ1. The four-domain simulation produces maximum is delayed and the vortex that eventually forms is weaker winds on the southeast ¯ank of the storm (Fig. 12d) in than its counterpart in CTRL. The storm is therefore agreement with reconnaissance observations near this not able to undergo appreciable self-ampli®cation time (Bosart and Bartlo 1991, see their Fig. 12c). As through air±sea interaction before it drifts over cooler expected, considerable structure exists in the four-do- water. main simulation that is not present at coarser resolution. While both simulations reveal banded precipitation structures, bands in CTRL-4D21 are more numerous and 2) 3-KM GRID SPACING narrower. The nest with 3-km grid spacing is inserted into do- The amplitude of asymmetries apparent in Fig. 12b main 3 (Fig. 1). When inserted into simulation CTRL, characterizes other times in CTRL-4D21. We show four it remains ®xed through 60 h. When inserted into I08, consecutive hourly depictions of rainwater mixing ratio the simulation with identical physical parameterizations and sea level pressure in Fig. 13. Beginning at 1900 as CTRL but begun at 0000 UTC 8 September, the UTC 9 September, a poorly organized mesoscale rain- greater movement of the storm requires that we allow band takes shape on the southeast ¯ank of the storm. domain 4 to move in a series of discrete jumps following The organizes as it is advected by the sym- the storm. Each jump is about 30 km and a total of metric circulation past the northeast quadrant of the about 5 jumps are needed to contain the storm. In all storm. Because the storm is moving northward, this cases, the fourth domain consists of 151 grid points in quadrant is the right-front quadrant, noted by other in- each horizontal direction. In the section that follows, vestigators as the locus of heavy rainfall in other cy- the suf®x -4D is added to the names of CTRL and I08 clones featuring signi®cant asymmetries (Burpee and to denote that they were run with four domains. Black 1989). However, because the deep tropospheric The initialization time of domain 4 proves to be im- shear vector, averaged within 100 km of the storm cen- portant. We delay the start of domain 4 to allow the ter, points toward the east-northeast during this period model to spin up features on domain 3 and thereby help (magnitude of about 0.8 ϫ 10Ϫ3 sϪ1, not shown), the determine the placement of the nest. Two nest initiali- area of intensi®cation of the rainband is almost directly zation times will be considered, 0900 UTC 8 September downshear. The outer portion of the rainband appears (simulation denoted CTRL-4D21) and 1200 UTC 8 Sep- to dissipate quickly, whereas the portion of the band tember (simulations CTRL-4D24 and I08-4D). The sig- nearer the center continues to rotate cyclonically and ni®cance of initializing at these two times is that they eventually dissipates over the southern ¯ank of the bracket a major eruption of convection on the meso- storm following 2200 UTC. scale, seen both in the observations and in CTRL (DB). Near and within the radius of maximum wind (40± Note that the fourth domain in I08-4D is initialized at 50 km), the rainwater maxima are generally coincident the same time as in CTRL-4D24, but only 12 h after with local minima in sea level pressure and enhanced the start of the three-domain integration (I08) from cyclonic circulation on scales of only about 15±20 km. which it is spawned. This behavior contrasts markedly with that outside the Figure 11 shows the time series of minimum sea level RMW where precipitation anomalies are typically as- pressure (SLP) for each of the simulations with a fourth sociated 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 sϪ1, long barbs 5 m sϪ1, and pennants 25 m sϪ1. plication is that convection outside the RMW produces buoyancy. This is consistent with the radial pro®le of cooling of the boundary layer, presumably through neg- azimuthally averaged and time-averaged relative hu- atively buoyant downdrafts, while convection near the midity (Fig. 14), which reveals that the mean humidity center produces downdrafts with reduced negative 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 Studies of intense hurricanes reveal the possibility km. The lack of cooling associated with the inner-core of mesovortices on the eyewall forming from baro- convection allows the dominant change in the mass and tropic instability (Schubert et al. 1999). However, since wind ®eld (see Fig. 13) to be lower pressure coincident the radial gradient of absolute vorticity is monotonic with a cyclonic ¯ow anomaly. In addition, the greater (not shown), such an explanation is unlikely in the absolute vorticity inside the RMW would enhance the present case. The vortices seen here appear to be fun- vortex stretching and ampli®cation rate of the meso- damentally tied to latent heating in convective bursts vortices closer to the storm center. near the eyewall. Similar mesovortices, collocated with

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FIG. 14. Time, azimuthally and vertically averaged relative hu- midity for CTRL and CTRL-4D21. Averaging time is from 51±60 h and averaging depth is from about 500 to 4 km MSL. re¯ectivity maxima, have been observed in developing tropical storms (Stewart and Lyons 1996) and in mature hurricanes (Marks and Houze 1984). However, the ob- served 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 spac- ing, only about half the RMW of the observed me- sovortices. These mesovortices proceed around the core, typi- cally 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 En- agonio (1998, 2001) and MoÈller and Montgomery (2000), wherein the axisymmetrization of localized anomalies of PV intensi®es the cyclone. The roughly continuous sequence of mesovortex formation and de- cay in favor of the symmetric circulation allows a nearly steady intensi®cation. That is not to say that in the ab- sence of vortices the storm would not intensify, but rather, that the formation of strong convective asym- metries appears to be the preferred mechanism of de- velopment in this case. This mechanism is clearly less pronounced at coarse resolution once the storm ap- proaches 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, al- FIG. 15. (a) Sea level pressure, wind at lowest model level (40 m though it exhibits considerable vertical tilt in the lower 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 sub- and middle troposphere toward the northwest with domain location. 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

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FIG. 16. Histograms of vertical motion (w) and the correlation of w at 3 km MSL with absolute vorticity ␩ averaged over the lowest 3 km MSL. (a) and (c) Statistics from a 9-km storm-centered grid (CTRL) that is 225 ϫ 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 w␩ over 3 ϫ 3 subdomains on the 3-km grid (see text for details). Units for w aremsϪ1 and for w␩ are 10Ϫ4 msϪ2. Statistics have been accumulated from 45 to 60 h for both simulations. Bin number refers to ranges of w and w␩ shown in legend at lower right. the RMW and reaches comparable strength to that constant), is an approximation to the stretching term in shown in Fig. 15. the vorticity equation and represents the rate of increase A central issue is why the simulations with a higher- of a vertical component of vorticity within the layer resolution domain each produce a weaker storm than from the surface to about 700 hPa. CTRL. Some insight is gained by a statistical analysis Figure 16 shows frequency histograms for both ver- of vertical velocity and the stretching term in the vor- tical motion and the stretching term obtained as follows. ticity equation. As was apparent from Fig. 15 in DB, The vertical motion and w␩ correlation are averaged the stretching term dominates the vorticity tendency. We over contiguous 3 ϫ 3 grids on domain 4 within a square analyze vertical velocity at the level nearest 3 km MSL area of 153 km on a side centered on the storm. For the

(wH) and the product of wH and absolute vorticity av- three-domain simulation, w and w␩ are computed at eraged over the layer beneath 3 km MSL (␩H). Because each grid point within the same area. By coarsening the the vertical velocity vanishes at the ground, the product ®elds on domain 4 by a factor of 3, the resulting quan- wH␩H/H, where H is the physical depth of the layer (a tities can be compared directly because they both rep-

Unauthenticated | Downloaded 09/24/21 09:07 PM UTC 1116 MONTHLY WEATHER REVIEW VOLUME 130 resent averages over a 9 km ϫ 9 km area. The histo- ing should incorporate nonhydrostatic effects which grams of w and w␩ shown in Fig. 16 represent a sum- limit vertical motion through the creation of a down- mation from 45 to 60 h. The bins, each representing a ward directed pressure-gradient force that acts against range of values for wH and wH␩H (the latter scaled by buoyant parcels. 104), are constructed to increase geometrically in width As one considers still coarser grid lengths, for ex- so as to de-emphasize the tendency for the quantities to ample, 27 km, there is a continued narrowing of the cluster about zero. vertical motion spectrum. Almost no downdrafts occur From Fig. 16, it is clear that the domain with 9-km and the ascending motions are weaker in D2. Moreover, grid spacing produces more numerous and stronger up- the mean vertical motion is much weaker in D2, only drafts with fewer and weaker downdrafts than on the 3- 1±2 cm sϪ1 versus 16 cm sϪ1 in CTRL. This latter fact km grid. Note the skewness of the distribution for the accounts for the notably weaker storm produced in D2 9-km grid, accentuating positive vertical velocities, and as compared with CTRL. the relatively symmetric appearance of the histogram In light of the comparison of vertical motion spectra for the 3-km grid, revealing less of a bias in wH. While over a variation of model grid spacing of a factor of 9, the consistently higher absolute vorticity present in we speculate that the bias in the area covered by upward CTRL (9-km grid) is partly responsible for the system- motion is roughly proportional to the grid spacing. In atically greater vortex stretching, it appears that much the limit that an extremely coarse grid spacing were of the discrepancy in the vortex stretching term (com- used (100±200 km grid spacing), the area used for av- pare Fig. 16b with Fig. 16d) is accounted for by the eraging in our simulations would reduce to a single grid differences in vertical motion between the two simu- point, and, the spectrum of vertical motion would reduce lations. In fact, the ratio of the time-averaged and area- to a single, positive value. averaged vertical velocity, 16 cm sϪ1 for CTRL and 8 However, the magnitude of the ascending motion ap- cm sϪ1 for CTRL-4D21, is about the same as the ratio pears to maximize for a grid spacing near the limit of of the stretching term in the two simulations. Without validity of the hydrostatic approximation. At ®ner grid a complete vorticity budget it is not possible to quantify spacing, nonhydrostatic effects become important, lim- the effects of the differing probability distributions of iting updraft strength. At coarser resolution two pro- vertical velocity on storm intensi®cation, but the qual- cesses act to limit the strength of upward motion. First, itative inference is that the biased distribution of w in the inverse dependence of vertical motion on length CTRL is the source of the greater intensi®cation rate scale (for hydrostatic motions) implies that vertical mo- and it may be physically interpreted as a relative absence tions should be weaker by a factor of 3 on a 27-km grid of convective downdrafts and an excess of upward mo- compared to a 9-km grid. Second, the weaker upward tion. motion on a coarser grid gives the cumulus scheme more The differences in vertical motion spectra are con- time to adjust the thermodynamic pro®le back to an sistent with the differences in lower-tropospheric hu- equilibrium, subsaturated state. It is therefore more dif- midity seen in Fig. 14 wherein CTRL-4D21 was sys- ®cult to achieve grid-scale saturation on a 27-km grid tematically drier than CTRL near the RMW. Although than on a 9-km grid. With less grid-scale saturation, a clear cause and effect is not evident, the presence of grid-scale overturning is relatively absent and strong more numerous and intense downdrafts would be ex- upward motion does not occur. pected in an environment of lower humidity and would The presence of stronger downdrafts with ®ner grid tend to maintain such a humidity state. However, the spacing currently lacks a purely physical explanation. more vigorous downdrafts in CTRL-4D21 at 3 km MSL However, spectral broadening is nearly always the result do not appear to penetrate into the boundary layer, judg- of adding degrees of freedom to a nonlinear ¯uid sys- ing from the nearly identical pro®les of ␪e within the tem. These additional motions are possible with the in- PBL in each simulation. The reduced humidity in the troduction of a ®ner grid spacing in a system dominated storm center in CTRL (inside a radius of about 30 km) by convective motions which seek the minimum re- is probably a consequence of the more well-de®ned solvable scale. This statistical-dynamical fact, coupled due to a greater storm intensity in that simulation as with the bias present in the vertical velocity distribution compared to CTRL-4D21. at coarser grid spacing, virtually guarantees stronger Weisman et al. (1997), in a study of squall line sim- downdrafts as resolution increases. ulations 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 4. Storm track spacing) as compared to the coarsened vertical motions a. Initialization time from the high-resolution simulations (1±4-km grid spacing). The stronger updrafts are attributed to im- In this section we consider three simulations initial- proper treatment of nonhydrostatic effects at coarse ized at 12-h intervals, 0000 UTC 7 September (I07), resolution. In our case, a 9-km grid spacing is still 1200 UTC 7 September (CTRL), and 0000 UTC 8 Sep- within the hydrostatic regime, whereas 3-km grid spac- tember (I08). Tracks for all three appear in Fig. 17.

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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±north- east 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 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 ¯ow at 850 hPa, averaged from about 70Њ to 80ЊWat30ЊN is 3±4 m sϪ1 , easily enough to account for the dif- ference in the position of the baroclinic zone by 1200 UTC 8 September seen in Fig. 18. The upper tropospheric ¯ow difference (CTRL Ϫ 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. FIG. 17. Tracks for I07, CTRL, and I08 along with the observed There is also a weak northerly ¯ow difference which storm track (Ls). 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 ®rst well-de®ned mesoscale These show a steady improvement in the track predic- cyclonic circulation near the surface coincides with the tion with later initialization time. We did not carry out region of warm advection at 850 hPa (and 700 hPa, not an integration from 1200 UTC 8 September or later, shown). In DB, it was shown how mesoscale lifting (and though we anticipate that there would not be continued attendant precipitation and latent heating) associated forecast improvement because most of the key features with warm advection and frontogenesis led to the pro- in the development (the upper-level trough and nascent duction of lower-tropospheric PV anomalies, which, in surface cyclone) were offshore and not captured by the turn, amalgamated into a nascent tropical storm. A sim- in situ observations. ilar evolution occurs here. The position of the region of Initialization at 0000 UTC 7 September (I07) pro- low-level warm advection appears to determine the ini- duces a storm which develops too far east and north. tial location of the mesoscale cyclogenesis. Because the Development in I07 began around 1800 UTC 8 Sep- location of lower-tropospheric warm advection is in er- tember, representing a lag of about 6 h relative to CTRL. ror in I07, so is the location of tropical cyclogenesis. Some hints of a secondary development in CTRL near Our ®rst attempt to simulate a storm beginning at the location of primary development in I07 are evident 0000 UTC 8 September was entirely unsuccessful in (not shown). This development occurs whether the sim- that no storm formed. Inspection of the lower- to mid- ulations are run with 2 or 3 domains, so the fact that tropospheric relative humidity ®eld offshore revealed this erroneous development occurs near a nest boundary excessive dryness with humidities averaging only 50%± (see Fig. 1) in both I07 and CTRL is not signi®cant. 60%. We modi®ed the humidity ®eld by replacing the An important difference in the upper-tropospheric relative humidity everywhere with the 12-h relative hu- ¯ow between I07 and CTRL is highlighted in Fig. 18. midity forecast from CTRL. This was done on domain Note that dynamically balanced ®elds, computed on do- 1 only (81-km grid spacing). This new humidity ®eld main 1, are presented. The amplitude of the trough over was interpolated to the higher-resolution domains and Florida at 1200 UTC 8 September is weaker in I07. the simulation begun (I08). The offshore humidity at There is also a more extensive southwesterly jet in I07 700 mb was greater than 80% over a large area in the over the region of cyclogenesis. These differences result reconstructed analysis. from a poorer handling of the trough fracture in I07 The result with the improved humidity is striking. compared to CTRL. Trough fractures have been studied The development of the tropical cyclone proceeds sim- in detail by Dean and Bosart (1996) wherein it was ilarly to that in CTRL, except that the track is much inferred that the process of trough fracture and cutoff improved. There is virtually no trace of the spurious low formation in the upper troposphere suffers from development over the northeastern portion of domain 3 inherently poor predictability. Examination of the conditions at 850 hPa indicates 2 The ¯ow difference displayed in Fig. 19a is computed after re- some important differences in the low-level structure, moving the upper-tropospheric PV anomalies from both I07 and particularly with respect to regions of warm advec- CTRL at 1200 UTC 7 September. The procedure is described in tion, which accompany the greater extent of trough 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 ϫ 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 1ЊC. in I08. As apparent in Fig. 17, the storm in I08 tracks the 39-h forecast from CTRL. At that time, the position westward almost to the Florida coast near Cape Canav- of the two storms is nearly the same, but the motion of eral, stalls, then turns northward. The timing of the the CTRL storm is slowly northwestward and the motion changes in storm motion follow closely the observa- of the storm in I08 is westward at about 6 m sϪ1 (Fig. tions, particularly the cessation of westward motion, 17). stalling, and commencement of northward motion. The To isolate the contribution of upper-level PV anom- improved track relative to CTRL allows precipitation to alies to storm motion in each simulation, we calculate reach the northeast coast of Florida much as depicted the total balanced ¯ow in each case (on domain 1). by Fig. 12 from BB. Then we recompute a balanced ¯ow with selected up- The reason for the improved storm track in I08 rel- per-level PV anomalies removed analogous to the ative to CTRL is primarily the differing behavior of the technique used to compute initial conditions in the upper-tropospheric PV. In CTRL, the upper-level cy- NOPV simulation (section 3a). The primary differ- clonic circulation is elongated from southwest to north- ence from the NOPV case is that the subdomain from east whereas in I08, it is more circular with more evi- which anomalies are extracted lies about 300 km fur- dence of easterlies on the poleward ¯ank of the positive ther east than the subdomain used to initialize NOPV PV anomaly (Fig. 20). In addition, the upper-level ridge owing to the motion of the synoptic-scale features in to the east of the storm is somewhat weaker and further the intervening time. We obtain four states of bal- east in I08 and a stronger, mesoscale ridge is evident anced geopotential and streamfunction. Only the immediately poleward of the storm. Here we focus on streamfunction will be used to derive the steering 0300 UTC 9 September, the 27-h forecast from I08 and winds and we denote the four streamfunction ®elds

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FIG. 19. (a) Relative vorticity from simulation I07 and difference in balanced, nondivergent (CTRL Ϫ I07) at 300 hPa for 1200 UTC 7 Sep (with upper-tropospheric PV anomalies removed,). Contour interval for vorticity is 5 ϫ 10Ϫ5 sϪ1 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 Ϫ I07) at 850 hPa for 1200 UTC 7 Sep. Contour interval for tem- perature is 3 K.

as ␺ C ,,␺*CI␺ I08 , and␺*08 , with capitalized portions of subscripts denoting the simulation and the asterisk denoting ®elds with the upper-level anomalies re- FIG. 20. PV and wind on 340 K surface for (a) CTRL and (b) I08 moved. The streamfunction ®eld representing the dif- at 0300 UTC 9 Sep. PV values greater than 1 PVU are shaded; heavy ference in upper-level PV within the chosen subdo- solid line is PV ϭ 0 contour. Wind symbols are plotted at every main is fourth grid point. ⌬␺ ϭ ␺ Ϫ ␺* Ϫ (␺ Ϫ ␺*). (4.1) CC I08 I08 quence of the relative shallowness of the PV anomalies in the core of the storm early in the development phase. We de®ne upper-level PV anomalies to lie at 400 hPa The majority of the diabatically produced PV resides and above. We average ⌬␺ between 900 and 450 hPa below 5 km, whereas at later times as the storm reaches to de®ne the steering ¯ow. hurricane intensity, the high PV extends to the upper It is not until 1200 UTC 8 September (24 h), as me- troposphere and the motion appears to match winds av- soscale cyclogenesis proceeds, that the concept of a eraged over a deeper column. steering ¯ow appears relevant. Even then, the layer over We de®ne storm motion at time t as the vector dis- which a reasonable match is found between vertically placement of the center between t Ϫ 1 h and t ϩ 1h. averaged wind and storm motion, roughly 900 to 450 The difference in storm motion at t ϭ 27 h (0300 UTC hPa, is relatively shallow compared with what is often 9 September) between the CTRL and I08 can be rep- used for hurricane motion. This is probably a conse- resented by the vector (Ϫ5.0, Ϫ1.5), 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 10Ϫ5 smϪ1 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 sϪ1. The difference represented by ⌬␺, interpolated to the location of each storm (the positions are nearly identical at 0300 UTC 9 September) results in a vector (Ϫ5.6, Ϫ0.6) or toward the west at about 5.6 m sϪ1. Thus, the difference in upper-level PV between CTRL and I08 within the subdomain accounts FIG. 23. PV and wind on 340 K from CTRL and BMJ1 1500 UTC for nearly all the difference in the steering ¯ow even 8 Sep (27 h). Plotting convention as in Fig. 20. though the PV anomalies included in the calculation reside entirely above the steering layer. tialization allows a better representation of the fracture The spatial pattern of ⌬␺ is displayed in Fig. 21. It clearly shows an anticyclonic anomaly poleward of the and the improved structure directly results in a better storm and a cyclonic anomaly equatorward of the storm, track prediction. This comparison points to the impor- yielding an easterly ¯ow between the two. This pattern tance of capturing the detailed structure of synoptic- is consistent with a more ``negative tilted'' trough in scale disturbances near the developing tropical cyclone. simulation I08, which in turn, appears related to the initial amplitude of the southern portion of the trough b. Cumulus scheme fracture that occurred on 6±7 September. The later ini- The storm track in BMJ1, GR, and EXP is more west- ward 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 reso- lution or greater), the total, area-integrated upward mass ¯ux is overestimated compared with simulations per- formed at cloud resolving resolution (Weisman et al. 1997). The reason is that (a) an entire 81 km2 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 ¯ux has direct implications for the upper- level potential vorticity, which, in turn, affects the ven- tilation ¯ow and storm track. The PV on the 340 K surface at 1500 UTC 8 Sep- FIG. 22. Tracks for simulations with different cumulus schemes tember from BMJ1 (representative also of GR and EXP) (CTRL omitted). is shown in Fig. 23 along with the analogous ®eld from

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PV which implies a superior treatment of precipitation and latent heating compared with CTRL. We have dis- counted this possibility in light of (a) physically unre- alistic 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 rep- resentation.

c. Other factors 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 Simp- son (1993) and the simpler two-category scheme of Du- dhia (1989). The maximum differences in storm position between either of these simulations and CTRL are less 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). than half of the differences described in sections 4a and 4b. Variation of the PBL schemes, SST, and use of coars- er and ®ner grid spacings produce still smaller differ- CTRL. The greater strength of both the cutoff low to ences in storm position. However, the relative insensi- the south and ridging to the north of the storm is ap- tivity of the track to the inclusion of ®ner resolution parent in BMJ1. The latter appears to result from greater may be underestimated due to the size of the innermost overall mass ¯ux in BMJ1, consistent with greater pre- domain, limited by computational constraints. To fully cipitation (Fig. 8) and stronger poleward out¯ow. The assess the effect of ®ner resolution on track, the inner- out¯ow displaces the tropopause upward and poleward, most domain should cover an area commensurate with creating an anticyclonic PV anomaly. The greater the diabatically induced, synoptic-scale PV anomalies strength of the cutoff low in BMJ1 is perhaps counter- responsible for steering. This would require a domain intuitive because one might expect that greater latent of 500±1000 grid points on a side. Such simulations are heating would result in more rapid weakening of cy- feasible, but beyond the scope of this work. clonic PV anomalies aloft. However, it appears from Fig. 23 that the enhanced convection in BMJ1 severs 5. Summary and conclusions the physical link between the PV anomaly over Florida and that at higher latitudes sooner than in CTRL. This The present study extends the results of DB by con- action appears to create a more circularly symmetric sidering changes in the intensi®cation and track brought cutoff low in BMJ1 than in CTRL. We speculate that about by changing initial conditions, boundary condi- the more circular anomaly is more resistant to defor- tions, representation of physical processes, and grid mation in the ensuing 12-h period than is the more elon- spacing within MM5. Strong sensitivities are found for gated anomaly in CTRL. varying SST, initialization time, boundary layer physics, Regarding the steering ¯ow, we compute an analo- cumulus parameterization, and grid spacing on the in- gous diagnostic to the one performed in section 4a to nermost nest. assess the difference in steering ¯ow between CTRL The goal of this paper has been to understand the and I08. Figure 24 shows ⌬␺ valid at 1500 UTC 8 dynamics that govern the differences in the intensi®- September (27 h, as shown in Fig. 23). The implied cation and track of Tropical Cyclone Diana that were difference in steering velocity is about 7 m sϪ1 toward seen among the various simulations. The precursor up- the southwest. Since the storm in CTRL is nearly sta- per-level disturbance is the catalyst for the tropical cy- tionary at 27 h, the motion of the storm in BMJ1 rep- clogenesis. When we remove the upper-level trough and resents the difference in storm translation during the ridge from the initial condition, no storm forms. As the period 24±30 h, an average motion toward the west- initialization time becomes later, the upper-level features southwest at about 10 m sϪ1. Thus, it is apparent that become better de®ned and the simulation improves. the differences in upper-level PV evolution once again When the model does not adequately forecast the upper- are a key factor in storm motion. In the present case, level trough fracture, such that the resulting disturbance changes in the precipitation physics result in changes retains a southwest to northeast tilt, the cold front re- in track through altering the upper-level PV and its as- mains too far north and the upper trough is weaker and sociated ventilation ¯ow. further north than observed. Warm advection along the It is tempting to argue that BMJ1, because of its better front and the associated tropical cyclogenesis thus occur track, had a more realistic treatment of the upper-level too far to the northeast.

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As the trough fracture becomes better resolved in the like the trigger for the Kain±Fritsch scheme, that is, they initial conditions, meaning more cyclonic PV breaks off introduce an effective parcel buoyancy that is propor- from the main westerlies, the anticyclone poleward of tional to the large-scale vertical motion. In section 3d, the system is able to attain a greater amplitude. Between it is argued that the widespread triggering of the Kain± the anticyclonic anomaly poleward of the storm and the Fritsch scheme is part of the reason that simulation cyclonic anomaly on the equatorward side, the deep- CTRL treats the initial storm intensi®cation fairly well; layer easterlies drive the developing cyclone succes- it reduces nonphysical grid-scale overturning on the 9- sively further west with later initialization time, im- km grid. proving the agreement with observations. When a fourth domain with a 3-km grid spacing is The effect of the choice of cumulus parameterization nested within domain 3 of simulation CTRL, the inten- on storm track can also be understood in terms of the sity prediction improves relative to that of CTRL. Com- effect on tropopause PV and the resulting changes in paring 9 km ϫ 9 km area averages from the 3-km and the deep-layer wind. In general, cumulus schemes that 9-km simulations, it is shown that the 3-km grid spacing allow greater and more widespread explicit precipita- produces notably more downdrafts and while some of tion, associated upward mass ¯ux, and divergent out¯ow the updrafts are also stronger, the overall spectrum of aloft result in more westward storm tracks. Use of the vertical motion is more symmetric about zero. The bias Betts±Miller±Janjic, Grell and explicit-only schemes on toward upward motion at coarser grid spacing is attri- the 9-km grid produce a more westward track compared buted to an improper treatment of nonhydrostatic ef- with the Kain±Fritsch scheme. While the more westward fects. Weisman et al. (1997) show that this produces track is in better agreement with observations, the track excessive upward mass ¯ux, and in the present context, is more erratic using schemes that produced more grid- results in excessive vortex stretching and spinup of low- resolved precipitation. The erratic behavior is due to the er-tropospheric cyclonic circulation. formation of numerous, intermittent, intense, mesoscale One of the notable differences seen on the 3-km grid (almost grid-scale) vortices 100±200 km from the es- is the development of intense mesovortices just inside tablished center. Because this behavior resembles the the radius of maximum wind. In many instances, these type of problems discussed in Molinari and Dudek are strong enough to bring the tangential wind to zero (1992) regarding grid-scale overturning at fairly coarse locally. Vortices persist for roughly 3 h (about one rev- resolution, we suspect that the improved track with the olution) and each is warm core. In some cases, the vor- Betts±Miller±Janjic and Grell schemes and with no cu- tices are strong enough that their formation and sub- mulus scheme may be fortuitous. This is especially true sequent absorption by the symmetric circulation cause in light of the fact that simply initializing 12 h later a steplike trace in the time series of central pressure, (0000 UTC 8 September) with the Kain±Fritsch scheme with each step corresponding to one vortex life cycle. produces the best track of all the simulations. Other factors such as SST, PBL scheme, and analysis Simulations with three domains using the Kain± of moisture in the initial conditions are important in the Fritsch scheme tend to intensify the storm too rapidly intensi®cation. These results are not surprising because after the incipient vortex achieves tropical storm such factors directly affect the amount of water vapor strength. The use of other cumulus schemes produce available for latent heat release and storm intensi®ca- storms weaker than observed. The Betts±Miller±Janjic tion. In general, results of varying the PBL physics agree scheme is unable to inhibit deep convection governed with Braun and Tao (2000). by the explicit precipitation scheme, primarily due to Overall, we ®nd that various choices of model ``phys- its lack of downdrafts, which limit the potential buoy- ics'' can produce a storm of almost any intensity, rang- ancy of boundary layer parcels. The Grell scheme, while ing from a marginal tropical storm to a mature hurricane. including downdrafts, does not activate enough to sup- It appears that a simulation more accurate than any dis- press grid-scale overturning. The worst results with a cussed in this paper could be obtained by a judicious 9-km grid spacing were obtained when the cumulus selection of grid spacing, initialization time, and model scheme is deactivated because the shortcomings seen in physical parameterizations, although this choice would simulations using Grell and Betts±Miller±Janjic are sim- not necessarily have either a physical justi®cation or ply magni®ed. evince success in other cases. Furthermore, such an op- The relative success of the Kain±Fritsch scheme is timization would be predicated on a single forecast mea- perhaps at odds with results from other studies wherein sure, and would likely change as one varies the measure the best results are obtained using the Betts±Miller± of forecast accuracy. Based on our results, we caution Janjic scheme (Liu et al. 1997; Braun and Tao 2000). against excessive tuning of model parameters to produce However, Braun and Tao simulate the genesis phase of a single simulation used for diagnosing atmospheric Hurricane Bob using a 36-km grid. At that grid spacing, phenomena. The more fundamental issue is investigat- the assumptions used in deriving the Betts±Miller±Jan- ing the nature of sensitivity, both physical and com- jic scheme may be more appropriate. Liu et al. (1997) putational, that is apparent from altering aspects of the use a version of the Betts±Miller±Janjic scheme on an simulation. 18-km grid, but modify the trigger function to be more It appears that, at least in the present case, despite

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