25.4 DEPENDENCE OF HURRICANE INTENSITY AND STRUCTURES ON VERTICAL RESOLUTION

Da-Lin Zhang and Xiaoxue WangDepartment of Meteorology, University of Maryland, College Park, MD 20742

1. Introduction

Rapid growth in computing power hasrecently allowed us to use small horizontalgrid length, even down to 1 – 2 km, tomodel the inner structures and evolution ofvarious mesoscale convective systems(MCSs). Indeed, increasing horizontalresolution with better model physicalparameterizations has shown significantimprovements in the quality of numericalweather prediction (NWP). However, theadequacy of vertical resolution in thecurrent NWP models has recently beenquestioned, and some studies indicatedthat increasing horizontal resolution alonedoes not always guarantee a bettersolution, particularly in the presence ofphase changes.

For example, Lindzen and Fox-Rabinovitz (1989) derived a consistencycriterion between horizontal and verticalresolution for quasi-geostrophic flows. Theypointed out that a fine horizontal resolution,without considering an appropriate verticalresolution, would lead to the production of‘noisy’ fields and may degrade the overallaccuracy of the solution. Based on a two-dimensional hydrostatic primitive equationmodel, Pecnick and Keyser (1989) deriveda relationship that physically relateshorizontal scales to vertical scales of anupper-level frontal structure. In contrast tothe above results that were obtained withdry dynamics equations, Persson andWarner (1991) studied the resolutionconsistency in a hydrostatic (moist)simulation of conditional symmetricinstability associated with frontal rainbands,and noted the development of spuriousgravity waves when the vertical andhorizontal resolutions are not consistent.

The purpose of this study is to examinethe sensitivity of explicit simulation of

Hurricane Andrew (1992) to varying verticalresolutions in terms of its intensity andinner-core structures. Liu et al. (1997; 1999)have shown a 72-h successful simulation ofthe hurricane track and intensity, as well asthe structures of the eye, the eyewall, spiralrainbands, the radius of maximum winds(RMW), and other inner-core features ascompared to available observations and theresults of previous hurricane studies. In thisstudy, the model set-ups, such as the modeldomains, grid sizes, initial conditions andphysics options, are the same as thoseused by Liu et al. (1997), except for thevertical resolution. The next sectiondescribes briefly the numerical model usedfor this study and experimental design.Section 3 shows sensitivity simulations,respectively. A summary and conclusionsare given in the final section.

2. Experiment design

In the present study, a two-wayinteractive, movable, triply-nested, cloud-resolving, non-hydrostatic version of thePennsylvania State University/NationalCenter for Atmospheric Research(PSU/NCAR) mesoscale model (MM5; seeDudhia 1993) is used. The triply nesteddomains have the (x, y) dimensions of 82 x64, 124 x 94 and 124 x 94 with the gridsizes of 54, 18 and 6 km, respectively. Themodel physics include (i) the Tao-Simpson(1993) cloud microphysics scheme for the6-km grid mesh, (ii) the Blackadar planetaryboundary layer (PBL) parameterization(Zhang and Anthes 1982) and (iii) a cloud-radiation interaction scheme (Dudhia 1989).The sea-surface temperatures (SST) areheld as constant in time during the 72-hintegration. The model is initialized at 1200UTC 21 August 1992 with a bogussedhurricane vortex. See Liu et al. (1997) formore details.

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In their simulation of Hurricane Andrew(1992), Liu et al (1997) used 23 vertical slayers. For the present study, we define acontrol run, in which 46 uneven half-s levelswith higher resolution in the PBL are used(Exp. CTL46). Several sensit ivi tyexperiments are designed to study theeffects of varying vertical resolutions on thesimulated hurricane intensity and inner-corestructures. In Exp. HRL69, 23 vertical layersare evenly added to CTL46, whereas inExp. LRL23 the CTL46 vertical resolution ishalved evenly. In addition, another threesensitivity experiments are conducted toexamine the effects of varying verticalresolutions in different portions of thetroposphere on the hurricane intensity andstructures: (i) use the same verticalresolution as that in Exp. CTL46 above themelting level (roughly at s = 0.44) butkeeping the same resolution as that in Exp.LRL23 for the layers below (Exp. HUT35,i.e., higher resolution in the uppertroposphere); (ii) use the same verticalresolution as that in Exp. CTL46 below themelting level but keeping the sameresolution as that in Exp. LRL23 for thelayers above (Exp. HLT35, i.e., higherresolution in the lower troposphere).

Fig. 1: Vertical distribution of half-s levelsfor each sensitivity experiment.Dashed lines denote roughly thelocation of melting layer.

and (iii) double the vertical resolution in thelowest 150 hPa layer, i.e., up to s = 0.845(Exp. HBL29). Fig. 1 illustrates thedistribution of the vertical s-layers for allsensitivity simulations. In the abovesensitivity simulations, all of the other modelparameters are kept the same as those inExp. CTL46. See Zhang and Wang (2003)for more details.

It should be mentioned that based onthe resolution consistency criterion (1), thevertical resolution for a grid size of 6 kmshould be about 60 m. Clearly, the highestvertical resolution used herein (i.e., Exp.HRL69) is still much coarser than thattheoretically required, but it has alreadypushed the existing computing power intothe limit. Thus, our study will be limited tothe highest vertical resolution possible withthe current computing resources that areavailable to us.

3. Results

In this section, we investigate the impactof varying vertical resolutions and time-stepsizes on the simulation of Hurricane Andrew(1992) in terms of its intensity, eyewallstructures and heating profiles.

Fig. 2 compares the time series of thesimulated minimum central pressures fromthe resolution sensitivity experiments. Notefirst that the simulated hurricane intensitiesdepart more significantly with time betweendifferent experiments; the maximumintensities could range from the deepest899 hPa in Exp. HRL69, to 907 hPa in Exp.CTL46 and the weakest 932 hPa in Exp.HUT35. The time series of central pressurefrom Exps. LRL23 and HRL69 are almostsymmetrically distributed above and belowthat of Exp. CTL46, respectively, with thedifference as large as 33 hPa in the first 60-h integration.

Second, increasing the verticalresolution in the low troposphere (HLT35)from LRL23 yields an intensity time seriessimilar to that of HRL69, only a few hPaweaker in the first 60-h integration, implyingthe significant effects of changing the lower-

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Fig. 2: Three hourly time series of theminimum central pressure from allsensitivity experiments.

level vertical resolution on the intensityprediction. Of interest is that increasingthe upper-level vertical resolution (HUT35)from LRL23 even produces the weakeststorm, i.e., 14 hPa weaker than that inLRL23, despite the use of more verticallayers. Of further interest is that theHUT35 time series follows closely that ofLRL23 during the first 30-h integration,deepens slightly from 30 – 36 h, butbecomes 10-20 hPa weaker than theLRL23 storm afterward. An examination ofthe model-simulated radar reflectivitymaps reveals that this bifurcation iscaused by different cloud structures in theeyewall and spiral rainbands as a result ofdifferent vertical resolutions. For example,the model generates a partial eyewall inHUT35, but a near-full eyewall in Exp.LRL23 with marked differences in sizeand rainband distribution from the 39-hintegration, which is just a couple of hoursbefore the crossover of the sea-levelpressure time series (cf. Figs. 2 and 3).Similarly, the time series in Exps. HLT35and HBL29 are similar to that of CTL46 inthe first 36 h, but then both becomesignificantly deeper. Despite the use ofless vertical layers in HLT35 and HBL29,their final intensities are close to theintensity in HRL69. The results suggest

that (i) increasing the vertical resolution inthe lower troposphere is more efficientthan that in the upper levels in deepeninga hurricane, and (ii) different partitioning ofa given number of vertical layers couldhave different impact on the deepeningrates and cloud structures in the eyewalland rainbands during the different stagesof hurricane development.

Fig. 3: Horizontal distribution of radar reflectivity,taken at s ª 0.785 (i.e., near 800 hPa), fromthe 39-h integration for (a) Exp. LRL23; and(b) Exp. HUT35.

The time series of simulated maximumsurface winds, given in Fig. 4, shows therelation of the simulated hurricane intensityto the surface layer resolution and frictionaleffects. The use of the thickest surface layer

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(80 m – at a full-s level) in Exp. LRL23produces the greatest maximum surfacewind of 75 m s-1 prior to landfall, whereasthe thinnest surface layer (about 27 m) inHRL69 has the weakest maximum surfacewind of 63 m s-1 in spite of its deepestminimum pressure (cf. Figs. 2 and 4). Thisis consistent with the notion that thefrictional effects would be more (less)pronounced if a thinner (thicker) surfacelayer of air mass interacts with the bottomsurface.

Fig. 4: As in Fig. 2, but for the maximumsurface winds.

The simulated radar reflectivity from the54-h integrations shows different inner-corestructures of clouds and precipitation amongthe various experiments (see Fig. 5). It isevident that the eyewall convectionbecomes more intense, more compact andmore symmetric with a wider annulus ofclouds outside as the vertical resolutionincreases from 23 to 69 layers. Differentinner-core cloud/precipitation structures alsoappear in the other three sensitivity runs.For example, the eyewall convection inHBL29 is also near-symmetric with moreconvection occurring to the west, whereasthere is a tendency to develop a partialdouble eyewall to the east in HLT35 (notshown), as also hinted from Fig. 2. Surfacerainfall amounts and distribution, includingmajor spiral rainbands, also differ between

the simulations (not shown). These resultsare all consistent with the simulatedintensity changes, as expected.

Fig. 6 display the height-radius crosssections of vertical motion superposed withthe in-plane flow vectors from the 54-hintegration. These maps exhibit a typicalhurricane structure: an intense radial inflowin the PBL, an outflow jet near the top of thePBL where the tangential winds are peaked,a slantwise updraft with a negative shear inhorizontal winds in the eyewall, and anoutflow layer in the upper troposphere. Ingeneral, the sensitivity of the simulated flowintensity to vertical resolution is consistentwith that of the minimum central pressure.For instance, increasing the upper-levelresolution (HUT35) has less notable impacton the height-radius distribution ofhorizontal winds and vertical motion, ascompared to LRL23. On the other hand,increasing the low-level resolution (i.e.,HBL29 or HLT35) generates the amplitudesof the low-level horizontal wind that aresimilar to those in CTL46, as expected.However, despite the development of amore intense storm in HBL29 (and HLT35),its associated upper-level outflows aresimilar to those in LRL23 but markedlyweaker than those in CTL46. This indicatesthe importance of designing a comparabledistribution of vertical resolution in studyinghurricanes’ inner-core structures. Betterresults tend to be obtained when high-resolution layers are used throughout thetroposphere.

When properly designed, increasingvertical resolution tends to increase themagnitude of vertical motion, for example,the maximum updraft varies from 2.5 m s-1

in LRL23 to 4.5 m s-1 in HRL69. Doublingthe low-level resolution (HBL29 and HLT35)can also duplicate somewhat the eyewallstructure and intensity shown in higherresolution runs (e.g., CTL46). Again,doubling the upper-level resolution (HUT35)from LRL23 affects little the verticalstructure and amplitude of vertical motion inthe secondary peak updraft, correspondingto the peak tangential wind and an outflow

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Fig. 5: Horizontal distribution of radar reflectivity, taken at s ª 0.785 (i.e., near 800 hPa), from the54-h integrations of all sensitivity experiments.

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Fig. 6: Height-radius cross sections of vertical velocity, at intervals of 0.5 m s-1, from the 54-hintegrations of all sensitivity experiments.

LRL23

CTL46

HBL32

HUT35

HRL69 HLT35

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jet, occurs near the top of the PBL in allhigh-resolution runs except in HUT35.This peak updraft does not seem to berelated to any computational instability,because this feature still appears whenthe time step of 13.3 seconds for thefinest 6-km resolution domain is reducedby half (i.e., 6.7 seconds); see Zhang andWang (2003) for more details. Thisfeature results more likely from theEkman pumping processes, which isassociated with the intense cyclonicvorticity generated by the peak tangentialwinds and a radial outflow jet near the topof the PBL (see Zhang et al. 2001), thatare then enhanced by diabatic heating.

Fig. 7 shows the storm-scaleaveraged heating profiles from eachsensitivity run which represent thecollective effects of deep convection onthe large-scale environment. Theseprofiles exhibit a deep layer of intenselatent heating up to an altitude of 13 km inthe eyewall, with a bimodal heatingdistribution: one associated with the low-level outflow jet and the other in theupper-level outflow layer. All these aresimilar to those shown in Zhang et al.(2002) except for their magnitudes due tothe use of different radii for the areaaverages. Evidently, the heating ratesdepend highly on the vertical resolution inthe same way as the storm intensity.Namely, the higher the vertical resolution,the more intense latent heating and astronger storm it is, since hurricanes aredriven by latent heat release. The heatingprofiles from the other runs, particularlyHRL69, are systematically much greaterin magnitude than those from LRL23 andHUT35 throughout the troposphere.Again, the vertical heating profiles fromExps. LRL23 and HUT35 are almostidentical in structure and magnitude;similarly among CTL46, HLT35 andHBL29 up to z = 7 km, as could beexpected from their similar resolutions inthe low troposphere.

While increasing the upper-levelresolution has little impact on the eyewallstructure, it does increase slightly the

Fig. 7: Vertical profiles of the latent heating rates (Kh-1) averaged within a radius of 150 km from the54-h integrations of all sensitivity experiments.

heating rates in the upper outflow layer (e.g.,HUT35 vs. LRL23, CTL46 vs. HLT35 andHBL29). This result appears to suggest thatthe use of higher vertical resolution helpstrigger the grid-box depositional growth(condensa t ion ) and sub l ima t ion(evaporation). For example, consider twoextreme cases for a given relative humidity:a very thick and a very thin layer. The grid-box saturation will likely occur first in the thinlayer if all the other conditions are identical.Of course, the decrease in truncation errorsleading to the generation of strongerdivergence, as the vertical resolutionincreases, may also contribute positively tothe magnitude of latent heating and thestorm intensity. Nevertheless, it is wellknown that the low-level heating maximumis more efficient than the upper-level one inspinning up mesoscale cyclones (Tracton1973; Anthes and Keyser 1979; Zhang et al.1988). The more intense low-level heating

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with the increased local resolution isconsistent with the increased hurricaneintensity.

4. Summary and Conclusions

In this study, several 72-h numericalintegrations are performed to study thesensitivity of the simulated Hurricane Andrew(1992) to various vertical resolutions andtime-step sizes using the nested grid, cloudresolving version of the PSU/NCARnonhydrostatic model (i.e., MM5) with thefinest grid size of 6 km. The vertical resolutionvaries from 23 to 69 layers, with varying layerthicknesses in the lower and upper portionsof the troposphere.

It is shown that changing verticalresolution has important impact on thehurr icane intensity and inner-corecloud/precipitation structures. Specifically,increasing vertical resolution tends tosimulate a deeper storm in terms of centralpressure, three-dimensional winds with moreprecipitation. For the vertical resolutionstested herein, the surface central pressurecould range from 932 to 899 hPa, theazimuthally averaged peak values of thetangential wind from 60 to 90 m s-1, the PBLinflow from 30 to 40 m s-1, the updraft from2.5 to 4.5 m s-1, and the diabatic heatingrates from 50 to 80 K h-1. Similarly, the low-level outflow jet and the upper-level outflowincrease significantly, both nearly double asthe vertical resolution increases from 23 to 69layers. Of importance is that the deepeststorm simulated could reach the maximumpotential intensity calculated from theprevailing sea-surface temperature, and thistrend would continue as the vertical resolutionfurther increases, indicating that someparameterized model physical processes(e.g., cloud microphysics or the PBL) may betoo sensitive to the vertical resolution.

It is found that increasing the verticalresolution in the low troposphere is moreefficient in intensifying a hurricane, whereaschanging the upper-level vertical resolutionhas little impact on the intensity prediction.

The former case could cause moredeepening of hurricanes because the low-level latent heating tends to induce moremoisture convergence in the PBL where thelatent energy source is originated. On theother hand, the increased latent heating inthe upper levels would cause theconvergence of the midlevel cold and dryair, suppressing deep convection in theeyewall. With higher resolutions in the lowtroposphere, the model produces a widereyewall, stronger spiral rainbands and awider area of precipitation as a result of amore intense low-level outflow jet beinggenerated. It is shown that the noisy flowsresulting from inconsistent resolutions foundin the previous studies are only notable inthe upper-level outflow where it is inertiallyless stable.

It is shown that the use of a thickersurface layer tends to produce the highermaximum surface wind; different surfacelayer thicknesses could produces themaximum winds ranging from 75 m s-1 (with80 m) to 60 m s-1 (with 27 m). This isconsistent with the notion that the frictionaleffects would be more (less) pronounced if athinner (thicker) surface layer of air massinteracts with the bottom surface. Thissuggests that a thin surface layer be used, ifpossible, to verify against observations at analtimeter level (z = 10 m).

In conclusion, it is highly desirable to usehigher vertical resolution when it is possible,together with higher horizontal gridresolution, to model more realisticallytropical storms and the other MCSs. Itshould be mentioned, though, that the aboveconclusion may not be applicable in certaincases in which most of precipitation isgenerated by convective parameterization incoarse-resolution models.

Acknowledgments

This work was supported by the NSF grantATM-9802391, the NASA grant NAG-57842,and the ONR grant N00014-96-1-0746.

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