16th Conference on Mesoscale Processes, Boston, MA, 2015.

Model physics influences on tropical cyclone size

Yizhe Peggy Bu and Robert G. FovellDepartment of Atmospheric and Oceanic Sciences, University of California, Los Angeles

ABSTRACT

Using a semi-idealized version of the operational Hurricane WRF (HWRF) model,we show that model physical parameterizations can dramatically influence TC size(width) as measured by the 34-kt near-surface wind radius. Enabling cloud-radiativeforcing and enhancing planetary boundary layer vertical mixing can both lead towider storms via encouraging more convective activity in the TC’s outer region, theheating from which broadens the wind field. These two processes can cooperate orcompete, and are dependent on favorable environmental conditions, complicatingthe evaluation of model physics improvements. An alternative approach to limitinghurricane inner core mixing in the GFS scheme without unrealistically discountingmixing outside the TC is presented.

1. Introduction

TC size is an important forecast metric forit directly and indirectly influences TC motion,intensity, track, and storm surge. In meteorology,there are a variety of metrics used to define the TCsize such as the radius of outermost closed isobar,the radius of vanishing wind and the radius of 34-knot (kt) wind speed. In this study, the radius of34-kt (about 17 m s−1) wind speed at 10 m abovemean sea level (MSL) is used to define the stormsize or width.

Bu et al. (2014) and Fovell and co authors(2015) demonstrated that the cloud-radiativeforcing (CRF), the interaction of hydrometeorswith longwave and shortwave radiation, has animportant role in expanding the storm radius.Averaged through a diurnal cycle, CRF consistsof pronounced cooling along the anvil top andweak warming through the cloudy air. Inparticular, the within-cloud warming was relevant,enhancing convective activity in the TC outer

core, leading to a wide eye, a broader tangentialwind field, and a stronger secondary circulation.This forcing also functions as a positive feedback,assisting in the development of a thicker and moreradially extensive anvil than would otherwise haveformed. CRF itself depends on the microphysicsparameterization and Fovell et al. (2010) showed itis a major reason why simulations can be sensitiveto microphysical assumptions.

Bu et al. (2014) also showed that the GFDL-derived radiation scheme employed operationallyin the Hurricane Weather Research and Forecast-ing (HWRF) model (Gopalakrishnan et al. 2012)since its inception did not handle CRF properly,resulting in deep clouds that were effectively trans-parent. However, testing revealed that implement-ing an ostensibly superior radiation scheme de-graded model skill. Analysis of those results led usto consider how planetary boundary layer (PBL)mixing influences storm size, in cooperation andcompetition with CRF.

It is widely appreciated that PBL processes

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play an important role in tropical cyclones(e.g., Smith 1968; Ooyama 1969; Emanuel 1986;Van Sang et al. 2008) and there have been manystudies addressing the sensitivity of simulatedTC to PBL schemes (e.g., Braun and Tao 2000;Hill and Lackmann 2009; Nolan et al. 2009a,b;Smith and Thomsen 2010). Most previous studiesfocusing on the PBL-TC relationship have focusedon TC intensity, inner core convection and/or theTC PBL structure. Our interest is in the influenceof PBL mixing on horizontal storm structure andsize, and we utilize the GFS PBL scheme becausethis is employed in the operational HWRF. Thisis a first-order vertical diffusion scheme basedon Troen and Mahrt (1986) and Hong and Pan(1996), which also gave rise to the commonly usedYSU PBL scheme.

In the GFS scheme, the PBL depth h isdetermined using an iterative bulk-Richardsonapproach calculated from the ground upward. Thevertical profile of momentum eddy diffusivity Km

is then obtained via

Km = k(U∗/φm)Z[α(1 − Z/h)2], (1)

where k is the von Karman constant (= 0.4),U∗ is the surface frictional velocity scale, φm isthe wind profile function evaluated at the top ofthe surface layer, and Z is the height above thesurface. This produces a mixing coefficient profilethat is parabolic in shape between the surface andheight h.

A recent addition is the tuning parameter, α,which was incorporated because Gopalakrishnanet al. (2013) determined the GFS scheme wasproducing a negative bias in storm intensityand positive bias in inner core boundary layerdepth in HWRF, a consequence of excessivelylarge Km values relative to those estimated fromobservations by Zhang et al. (2011b). Figure1, taken from Gopalakrishnan et al. (2013),demonstrates how the α parameter can controlthe simulated Km as a function of wind speed.While a value of α = 0.25 (Fig. 1b) was foundto produce the most reasonable results relative tothe observations for wind speeds in the range 10 -

60 m s−1, a value of α = 0.7 was adopted in the2013 and 2014 operational versions of HWRF in allthree of its telescoping domains as a consequenceof detailed skill testing against retrospective TCcases.

Fig. 1. The variation of the eddy diffusivitycoefficient at about 500 m MSL with 10-m wind speedfrom high-resolution HWRF model output (grey dots)using α values of (a) 1, (b) 0.5, and (c) 0.25, comparedwith observationally-derived values from Zhang et al.(2011a) (purple crosses). From Gopalakrishnan et al.(2013).

2. Model and experimental design

The simulations of this study are carriedout using the 2013 version of the HWRFmodel, similar to that used in Bu et al.(2014). These experiments are “semi-idealized”

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in that we dramatically simplified the operationalconfiguration to exclude land and decouple theocean model, employ a uniform and constant sea-surface temperature (SST), and initialize witha horizontally homogeneous tropical soundingwithout any mean flow. The “bubble” proceduredescribed in Cao et al. (2011) was used to initiatethe TC. All HWRF simulations spanned fourdays and composite model fields were constructedfor the fourth day in a vortex-following fashion,averaging over one full diurnal cycle, and all fieldsshown herein are azimuthally averaged.

As in Bu et al. (2014), we adopted the2012 HWRF design of three telescoping domains(with 27, 9 and 3 km horizontal grid spacings)along with some of the operational modelphysics used during the 2013 season, such asthe SAS (Simplified Arakawa-Schubert) cumulusparameterization (in the 27 and 9 km domainsafter 24 h) and the aforementioned GFS PBLscheme. The “operational configuration” alsoconsisted of a tropical variant of the Ferrier et al.(2002) microphysical parameterization (MP) andthe GFDL radiation package; this is compared toruns made using the Thompson et al. (2008) MPand/or RRTMG radiation (Iacono et al. 2008).

3. Results

a. Cooperation with CRF

As mentioned above, Bu et al. (2014)demonstrated that CRF plays an importantrole in determining TC structure. EnablingCRF can increase the storm size (as manifestedby the 34-kt radius of the 10-m wind speed)by a substantial (and MP-dependent) amount(compare thin blue and thin red contours in Fig. 2)because hydrometers interacted with radiationto force gentle ascent, elevating the relativehumidity through a deep layer mainly above thePBL. When the RRTMG scheme was employed,both the operational (Ferrier) and a moresophisticated (Thompson) microphysics schemespermitted generation of realistic patterns of SWwarming and LW cloud-top cooling and within-

Cat. 3

Cat. 2

Cat. 1

34-kt

Radius (km)

10-m

win

d sp

eed

(m/s

)

Fig. 2. Radial profiles of the azimuthally-averaged 10-m wind speed from semi-idealized HWRFsimulations using Ferrier MP with GFDL radiationand α=0.7 (operational configuration; thin bluecontour); RRTMG radiation and α=0.7 (thin redcontour); RRTMG and α=0.25 (thick red contour);and GFDL and α=0.25 (thick blue contour). Blackdots indicate 34-kt wind radii.

cloud warming, with variations in pattern andmagnitude reflecting the different assumptionsemployed by the MPs (shown for Thompson inFig. 3a). Note there is no effective CRF with theoperational GFDL radiation package (Fig. 3b).

After we identified the CRF issue, the Devel-opmental Testbed Center (DTC) and the HWRFteam evaluated the RRTMG scheme along withThompson microphysics for adoption in the oper-ational HWRF. Analyses of retrospective simula-tions demonstrated that the HWRF forecast skillwas generally degraded when the new physics wasincluded and, as a consequence, neither packagewas adopted for the 2014 TC season. Our analy-ses of their experiments led us to realize that bothCRF and PBL mixing have potentially profoundinfluences on storm structure, which can directlyand indirectly influence intensity and track fore-cast skill. In brief, CRF encourages convectiveactivity in the outer core via gentle lifting abovethe PBL, but outer region convection can also re-

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sult from enhanced vertical mixing within the PBL– controlled by the α parameter – which carriesmoisture from the sea surface to the top of theboundary layer. In both cases, the enhanced con-vective activity in the outer region broadens thewind field, as shown by Bu et al. (2014) and Fovelland co authors (2015).

It emerges that these two processes, CRF andPBL mixing, can cooperate or compete. Recallthat Gopalakrishnan et al. (2013) recommended avalue of α = 0.25 in (1), but 0.7 was selected foroperational use. Our working hypothesis was thatthis increased α inadvertently compensated for themodel’s tendency to produce overly small TCs,which was actually a consequence of the missingCRF. Therefore, when the radiation problemwas fixed, the model was left with a fairlyconsistent positive size bias that led to worse skillscores1. Put another way, we believe that a properimplementation of CRF would justify a smallerand more defensible (based on the observations)value of vertical eddy mixing in the GFS PBL.

We now demonstrate that CRF and α havequalitatively similar influences on horizontalstorm size. Figure 2 also shows the effect ofdifferent combinations of CRF and PBL mixing onTC width for Ferrier-based storms. Note varyingα (for fixed CRF) causes the 34-kt wind radiusto increase by about 75% independent of theradiation scheme employed (compare thick andthin contour pairs). The narrowest storm usedthe α = 0.25 value suggested by Gopalakrishnanet al. (2013) with GFDL radiation, while thewidest employed the operational setting (0.7)with RRTMG. Thus, it is seen that the physicsinterplay between CRF and mixing can alter the34 kt wind radius by factor of two, which isdramatic. There is a material impact on the eyesize as well.

1Among the 2012 retrospective hurricanes examined,the positive size bias was readily apparent amongthe Atlantic storms. In the East Pacific, theThompson/RRTMG cases tended to exhibit positive biasesearly on, but also encountered colder SSTs earlier, resultingnegative size biases at longer forecast lead times.

HWRF Thompson/RRTMG - condensate and net radiation

C

W

radius (km)

heig

ht (k

m)

(a) CRF-on

(b) CRF-o�

mixing ratio (g/kg)

Fig. 3. Total condensation (shaded, note logarithmicscale) and net radiation (negative [dashed] contourinterval 0.1 K h−1, and positive [solid] interval 0.05K h−1) for Thompson storms with (a) RRTMG, and(b) GFDL radiation. C and W stand for cooling andwarming, respectively. From Bu et al. (2014).

b. Eddy diffusion and storm size

1) Sensitivity to α

The foregoing result occurs because thePBL mixing acts in a very similar manner asCRF in expanding storm size, as illustrated inFig. 4, which also focuses on the Ferrier MP.The shaded field is net diabatic forcing owingto microphysics, temporally and azimuthallyaveraged. Implementing CRF for fixed α (leftcolumn) and varying α for fixed CRF (rightcolumn) both result in a radially expanded heatingfield, causing the wind field (as illustrated bytangential wind differences in the bottom row) toexpand. Note that for this MP, sensitivity to αexceeds that for CRF, as was suggested by thenear-surface wind profiles (Fig. 2).

The α parameter was added to (1) to control

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Fig. 4. Radius vs. height cross-sections showing the symmetric components of microphysics diabatic forcing(shaded at K hr−1) and tangential wind (contoured at 10 m s−1) from Ferrier MP simulations and α=0.7 forthe (a) RRTMG radiation and (b) GFDL radiation cases. Panel (c) shows the RRTMG minus GFDL differencefields; the superposed field is tangential velocity difference (1 m s−1 contours). Also shown are simulationsusing Ferrier MP and RRTMG radiation with (d) α=0.7 and (e) α=0.25. Panel (f) shows the α=0.7 minusα=0.25 difference fields.

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eddy mixing in the hurricane inner core. Owing toits implementation, mixing is reduced throughoutthe hurricane and beyond. Figure 5 shows verticalprofiles of Km, averaged over an annulus residingbetween 30 and 200 km from the center for variousα values, with the corresponding near-surfacewind profiles presented in Fig. 6. The simulationsin these figures employed Thompson MP, RRTMGradiation, and CRF was active, along with ourdefault sea surface temperature (SST) of 302.5K. Note that the Km profiles differ little withrespect to vertical shape, which is determined by(1) and the PBL depth h. Varying α from 0.25to 1.0, however, causes the storm size to increasemonotonically from 150 km to 250 km.

One important and direct impact of the eddymixing is associated with the vertical transportof water vapor in the boundary layer, upwardfrom the sea surface to the PBL top. Figure7 presents averaged vapor and Km fields forThompson/RRTMG storms with α=0.7 and 0.25,along with their differences. Note the latterdemonstrate that the more substantial mixingproduced with larger α is associated with highermoisture contents in the upper portion of thePBL, especially at larger radii. This patternis consistent with the contribution of verticaleddy mixing to the local vapor tendency, whichis a second-order parabolic term (Klemp andWilhelmson (1978)) of the form[

∂q

∂t

]mix

=∂

∂zKh

∂q

∂z(2)

where q is the water vapor mixing ratio, zis the height, and Kh is the vertical diffusionapplied to scalars such as moisture and potentialtemperature (and nearly identical to Km for thesesituations).

In the atmosphere, the water vapor concentra-tion decreases quasi-linearly with height and, asa consequence of the parabolic vertical shape ofKh, we would expect negative vapor tendencieswhere Kh increases with height (below the levelwhere Kh reaches its maximum) and positive ten-dencies where Kh decreases with height (above the

Fig. 5. Vertical profiles of eddy diffusivity (Km,m2 s−1) averaged from radius of 30 to 200 km ofsimulations using GFS PBL scheme with α=1.0 (red),α=0.7 (green), α=0.4 (blue), and α=0.25 (yellow).

Kh maximum). This also applies to the differencefields, and explains the positive values above, andnegative ones below, the level of maximum Km

difference (Fig. 7c). Thus, one contributor leadingto the greater PBL moisture (≥ 400 m above thesea surface) in the larger α run is enhanced verti-cal mixing. The enhanced water vapor transportto the top of the PBL brings the air there closerto saturation, which can encourage more convec-tive activity, producing the diabatic heating thateventually leads to a broader wind field.

2) Sensitivity to SST

Examination of DTC’s HWRF retrospectivecases from their initial Thompson/RRTMG testsdescribed above suggested to us that the impactof α could vary from case to case, and evenfrom region to region, with some storms beingquite insensitive to the value employed. Fromthese cases, we surmised that the less convectivelyfavorable the environment, the less influence eddy

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Fig. 6. 10-m wind speed(m s−1) as a function of theradius of simulation with α=1.0 (red), α=0.7 (green),α=0.4 (blue), and α=0.25 (yellow).

mixing of moisture would or could have. Withinthe semi-idealized framework, we can establisha less favorable environment for convection bysimply lowering the SST. In this section, weexplore how SST controls the impact of α on thestorm size.

For example, when the sea surface is cooledby 2.5 K (Fig. 8b), to 300 K, the size differencebetween the α=0.7 (black curve) and the α=0.25(red curve) storms is smaller than when the SSTwas set to 302.5 K (Fig. 8a). (Curiously, theintensity difference is larger at this more moderatesurface temperature; we speculate about thisbelow.) When the SST is further reduced to 298K, the TC size difference almost vanishes (Fig. 8c).Figure 9 presents the vapor and Km differencefields between large and small α runs for thesetwo cooler SSTs, for comparison with Fig. 7c. Theoverall patterns are similar but the magnitudes aresmaller. Reduced eddy mixing, especially in theouter core region, leads to reduced vertical vaportransport, resulting in less convective activity. Asa result, other factors being equal, the wind fieldcould not be expanded as much.

Thus, it appears that TC size can be directly

24

23

22

21

19

18

17

16

15

14

13

12

11

10

9

8

7

6

mix

ing

ratio

(g/k

g)

Hei

ght (

km)

8

4

2

1

0.5

0.25

0.125

-0.125

-0.25

-0.5-1

-2

-4

-8

-16

radius (km)

a) α=0.7

b) α=0.25

c) α=0.7 - α=0.25

Fig. 7. Radius vs. height cross-sections showingthe symmetric components of water vapor (shaded, gkg−1) and eddy diffusivity applied to vapor Kh (10 m2

s−1 contours), for Thompson/RRTMG simulationsusing (a) α=0.7; (b) α=0.25; and (c) the differencesbetween the two. Simulations used SST=302.5 K.

modulated via water vapor transport in theboundary layer, with the size differences betweenthe TCs produced by larger and smaller α valuesgradually disappearing as the entropy supply fromthe sea surface is reduced. The inclusion oflower sensitivity cases could serve to obscure theinfluence of α somewhat in ensemble statisticsspanning a large number of events. In contrast,the intensity differences emerge as somewhat morecomplex. Greater vertical transport in the outercore region will always encourage larger TCs, butTC intensity can be influenced by the competitionbetween the strength of the convection in theeyewall and outer core regions. Though decreasingthe water vapor diffusion through the whole

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radius (km)

10 m

tang

entia

l win

d sp

eed

(m/s

)

a) 302.5 K

b) 300 K

c) 298 K

a=0.7

a=0.7

a=0.7

a=0.25

a=0.25

a=0.25

Fig. 8. 10-m wind speed (m s−1) as a functionof radius for Thompson/RRTMG simulations withα=0.7 (black) and α=0.25 (red) and (a) SST=302.5K; (b) SST=300 K; and (c) SST=298K.

domain may suppress the convection in the eyewallregion somewhat, the outer convection may bereduced even more. As a consequence, the netinfluence may be to actually intensify the TC. Thiswould require further study.

c. An empirical cap for eddy diffusivity

1) Motivation

As mentioned above, the operational HWRF’sGFS PBL scheme can produce values of eddymomentum diffusion (Km) that are much greaterthan suggested by observations (Zhang et al.2011a,b; Gopalakrishnan et al. 2013), especiallywhen the wind speeds are large. To amelioratethis, the α factor was introduced into the eddydiffusivity equation (1) to tune the PBL-generated

Fig. 9. As in Fig. 7c, but showing vapor andKh difference fields between α=0.7 and α=0.25simulations with (a) SST=300 K; and (b) SST=298K.

mixing, although a larger value for this parameterthan suggested by the observational comparisonwas eventually adopted for the operational model.We have shown that α not only can stronglymodify TC inner core structure, but also mayinfluence the outer wind field. However, theadoption of this mixing reduction factor comeswith some problems.

First of all, the imposition of a constant αvalue does not guarantee that Km will not exceedthe observed values in some cases and at somewind speeds. Additionally, it introduces anothermodel “knob” that requires tuning, and the αvalue which is optimal for the inner core regionmay not be best for the outer core region. Whenα = 0.7, the simulated storm might be too weakwith an excessively deep PBL. A value of α = 0.25might lead to the storm with the correct intensitybut is too narrow. It is likely impossible to get auniversal α value which can “fit” for every case.

Most worrisome of all, this original implemen-tation of α means that eddy mixing is reduced rel-

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ative to the default GFS scheme not only withinthe hurricane inner core but also through the en-tire domain. That is, α affects mixing over theocean far from the TC, and over land, places wherethe PBL scheme should not be modulated (if thescheme is fundamentally accurate). To addressthese issues, we have designed a new computa-tional algorithm to limit the vertical mixing in theTC’s inner region as indicated by the observationsbut without artificially constraining the scheme inthe surrounding environment or changing the ver-tical shape of the eddy diffusivity profile generatedby the PBL scheme. The new scheme is appliedonly over water, and even then is likely to acti-vate only when wind speeds of the kind found inhurricane inner cores are encountered, leaving thePBL scheme unmodified for the vast majority ofgrid points.

2) Approach and implementation

This is achieved through imposition of a windspeed-dependent upper bound on Km based onthe diagnosed eddy diffusivity at 500 m MSLderived from the Zhang et al. (2011b) observations(Fig. 1). According to the correlation betweenthe wind speed (WS) and the Km value at 500m as revealed in Fig. 10, we consider WS/0.6 asa simple, observationally-suggested, and empirical“cap” for Km to enforce an upper bound on eddymixing based on wind speed, which will act tolimit Km in the inner core where wind speeds arelarge. In this strategy, α in (1) is transformedinto a wind speed-dependent reduction factor thatwill vary from column to column, being effectivelyinactive (i.e., α = 1) in many of them. Thestrategy is carried out via the following steps, withsome possible scenarios depicted in Fig. 11.

First, we determine the wind speed at themodel level nearest 500 m above the surface ineach model column and then calculate Km(cap)as WS/0.6 for that column. Next, the first guessKm is computed by the PBL scheme using (1)without modification (α = 1). If Km at 500 m ≤Km(cap) for any reason, then Km remains at its

Fig. 10. Same as Fig.1c, but the red dashed lineof Km=WS/0.6 superimposed by the authors as theproposed wind speed-based limit on Km.

first guess value and mixing is unrestricted. [Asillustrated in Fig. 11a and b, it does not matterthat Km might exceed the capping value above orbelow 500 m, as the observations only constrainthe mixing at the 500 m level]. If, however, Km at500 m exceeds the cap, then the α for that columnis Km(cap)/Km(500 m). This α is then appliedthrough the entire PBL within that model columnto shift the eddy diffusivity profile leftward (tosmaller mixing coefficient values) without changeof shape (as illustrated by the dashed curves inFig. 11c and d). Note that this strategy permitsthis “effective α” to vary in space.

3) Results

Figure 12a presents a scatterplot of wind speedagainst the eddy mixing at 500 m MSL for semi-idealized Ferrier/RRTMG simulations, averagednot only temporally and azimuthally but alsothrough a 150 km wide annulus extending outwardfrom the radius of maximum wind (RMW). Bydesign, the capped Km profile (purple) does notexceed the WS/0.6 limit (dashed) although thereis nothing to prevent Km from being less than thecap. In this particular situation, the α=0.4 caseroughly follows along the WS/0.6 limit, but thisis strongly case-dependent (see below) and thusnot guaranteed. As α gets larger, Km increasesat a faster rate as wind speed strengthens, and αvalues such as 0.7 and larger result in very large

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500 m

Zoriginal

a)

500 m

original

b)

500 m

Z

Km cap

original

Km

adjusted

c)

500 m

Km cap

original

Km

adjusted

d)

Fig. 11. Depiction of Km adjustment based onKm(500 m) and Km(cap) for scenarios in which: (a)the height of maximum Km is below 500 m butKm(500 m) < Km(cap); (b) the height of maximumKm is above 500 m but Km(500 m) < Km(cap);(c) the height of maximum Km is below 500 mand Km(500 m) > Km(cap); and (d) the height ofmaximum Km is above 500 m and Km(500 m) >Km(cap). The dashed red line is the capping valuebased on wind speed at 500 m, and in (c) and (d), theadjusted Km profiles are the blue dashed curves.

eddy mixing for all wind speeds.As could be anticipated, the 10-m wind profile

of capped Km case resembles α=0.4 for thisparticular case (Fig. 13). The storm intensityand the radius of the 34-kt wind speed producedby these two storms are almost identical. α=1and α=0.7 produce much broader wind fieldswhile α=0.25 produces the narrowest wind field,consistent with what suggested by their differentKm profiles. Figure 14 depicts the inflow layerstructures of these TCs, plotted with respectto radius normalized by the RMW. Consistentwith the results of Gopalakrishnan et al. (2013),restricting Km effectively decreases the boundarylayer depth at inner core region, and the capped

Km = WS/0.6

α=0.5α=0.4

α=0.7

(b) Hurricane Daniel (04E/2012, 070406)

α=0.25

α=1.0

Capped Km

wind speed at 500 m (m/s)Km

(m2 /

s) a

t 500

m

Capped Km

α = 0.25

α = 0.7

α = 0.5

α = 0.4

Km vs. wind speed @ z=500 m (F/RRTMG)(a) Semi-idealized

α = 1.0

Km = WS/0.6

Km (m

2 /s)

at 5

00 m

Fig. 12. Eddy diffusivity (m2 s−1) vs. wind speed (ms−1) at 500 m for simulations using Ferrier/RRTMGwith Capped Km (purple) and various values of α for(a) semi-idealized runs with 302.5 K SST; (b) real-data runs of Hurricane Daniel (2012 04E), initializedon 04 July at 0600 UTC.

Km inflow structure appears acceptable relative tothe Zhang et al. (2011b) category 1-5 composite.

The effect of capped Km is case-dependent,which can represent an advantage of this strategyover the original α approach in that it will notlimit mixing in situations in which it might notbe excessive. Figure 12b presents results from2012 hurricane Daniel, a relatively weak EastPacific case, also made using Ferrier and RRTMG.Relative to the semi-idealized experiment, smallerKm values were generated at each value of WSand α. The capped Km effectively limited mixingin most of the storm inner core, as evidenced bymixing not exceeding the WS/0.6 line, but notas severely as single values of α < 0.7 would have.The capping implies that α was allowed to increasetowards one as radius increased from the RMW,which is a logical result.

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Fig. 13. 10-m tangential wind (m s−1) forsimulations with Ferrier MP scheme and α=1.0(yellow), α=0.7 (blue), α=0.4 (green), α=0.25(black), and capped Km (purple).

This modified GFS PBL has been providedto the HWRF developers and tested againstretrospective cases. As part of a suite of physicsimprovements (including the adoption of RRTMGradiation), the modification has been found toimprove forecast skill. As a consequence, themodification has been incorporated into the 2015version of the operational HWRF model.

4. Summary and conclusion

Bu et al. (2014) demonstrated that cloud-radiative forcing (CRF) can exert a substantialinfluence on numerically simulated TCs, especiallywith respect to the storm’s horizontal scale. Wefurther demonstrated that the radiation schemeemployed by the operational HWRF model, whichderived from the old GFDL parameterization, wasvery deficient in handling CRF, to the point thatit was essentially absent. However, when theHWRF model was applied to historical cases usinga more realistic radiation package, model skill withrespect to important storm characteristics suchas intensity, position and size was found to bedegraded. Our investigation of this phenomenon

led us to focus on the planetary boundary layer(PBL) scheme and how it was also influencingstorm size, in cooperation and competition withCRF.

Specifically, we found TC structure and inten-sity to be sensitive to the PBL parameterization,particularly the manipulation of the magnitudeand vertical structure of the eddy mixing. Ob-servations suggested that this mixing as producedby the GFS PBL scheme used operationally in theHWRF model to be excessive, with the boundarylayer depths it identifies also being too deep, atleast within the hurricane inner core. The PBL-generated mixing in this scheme can be tuned viathe parameter α, which was added several yearsago to (1), the equation that generates the verti-cal profile of momentum diffusivity. In the cur-rent operational model, α is set to 0.7, althoughGopalakrishnan et al. (2013) suggested α=0.25 asyielding Km values and PBL depths that are moreconsistent with the observations. The larger valueof α was selected because it improved the forecastskill of the operational model.

Our analysis suggested that the large value ofα used in the operational model was essentiallycompensating for the lack of cloud-radiativeforcing in the HWRF model. As a consequence,when the radiation issue was fixed, the model TCsdeveloped a positive size bias, leading to poorerintensity and position forecasts. At this point,two things become important: to explain howand why PBL mixing influences storm size, andto identify a better, more surgical approach tolimiting mixing within the hurricane inner core.

We have come to appreciate that the PBLscheme influences storm size indirectly, in amanner that is actually very similar to theimpact of CRF. Eddy mixing of water vaporhelps to transport water to the top of theboundary layer. There, the relative humidityis elevated, and convective activity is provoked– presuming environmental conditions (moisturecontent, vertical stability) – are sufficientlyfavorable. The convective activity indirectlyexcited by the vertical moisture transport

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Normalized radius (multiples of RMW)

a) α=0.25

b) α=0.4

c) α=0.7

d) Capped Km

Hei

ght (

km)

Radial velocity (m/s)

Fig. 14. Radial wind (shaded, m s−1) and tangential wind (contoured, m s−1) versus radius (expressed asmultiples of the RMW) for simulations using Ferrier/RRTMG with α equal to (a) 0.25; (b) 0.4; and (c) 0.7;and (d) capped Km. Solid blue line indicates the PBL depth, based on the 10% of the maximum inflow speedcriterion. Black dashed line crudely depicts inflow depth from a Zhang et al. (2011b) category 1-5 composite(their Fig. 10).

generates the heating that broadens the wind field.Thus, a compelling parallel is seen with respectto CRF, the difference being that the heatingassociated with in-cloud warming was focusedabove the boundary layer while the PBL influenceis essentially bottom-up.

Examination of retrospective cases made usingthe HWRF model suggested to us that TCs arenot always sensitive to α. We have come tounderstand that the sensitivity is diminished whenthe TC environment is generally less favorable.We demonstrated that via experiments in whichthe sea-surface temperature (SST) was reduced.Lower SSTs mean smaller moisture availabilities,and less vertical moisture diffusion, other factorsbeing equal. Our analyses indicate that thevertical moisture flux is the controlling factor.

Within the GFS PBL scheme, the currentimplementation of the α factor to control excessive

hurricane core mixing is attractively simple buthas some serious deficiencies, as noted above. Wedeveloped new computational method to preventKm from being too large when the wind speed ishigh in a manner that also prevents the schemefrom artificially suppressing mixing beyond thehurricane inner core. This scheme was adoptedfor inclusion in the 2015 release of HWRF and hasbeen selected for the operational configuration.

Acknowledgments. The authors gratefully acknowl-edge the assistance of Drs. Ligia Bernardet, MrinalBiswas, Gregory Thompson, Christina Holt, andVijay Tallapragada, and the support of the De-velopmental Testbed Center. This work was sup-ported by the National Atmospheric and OceanicAdministrations Hurricane Forecast ImprovementProgram (HFIP) under Grant NA12NWS4680009

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and by the National Aeronautics and Space Ad-ministrations Hurricane Science Research Programunder Grant NNX12AJ83G.

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