Analysis of Idealized Tropical Cyclone Simulations Using

Analysis of Idealized Tropical Cyclone Simulations Using the Weather Research andForecasting Model: Sensitivity to Turbulence Parameterization and Grid Spacing

KEVIN A. HILL AND GARY M. LACKMANN

Department of Marine, Earth and Atmospheric Sciences, North Carolina State University, Raleigh, North Carolina

(Manuscript received 12 April 2007, in final form 2 January 2008)

ABSTRACT

The Weather Research and Forecasting Advanced Research Model (WRF-ARW) was used to perform

idealized tropical cyclone (TC) simulations, with domains of 36-, 12-, and 4-km horizontal grid spacing.

Tests were conducted to determine the sensitivity of TC intensity to the available surface layer (SL) and

planetary boundary layer (PBL) parameterizations, including the Yonsei University (YSU) and Mellor–

Yamada–Janjic (MYJ) schemes, and to horizontal grid spacing. Simulations were run until a quasi-steady

TC intensity was attained. Differences in minimum central pressure (Pmin) of up to 35 hPa and maximum

10-m wind (V10max) differences of up to 30 m s21 were present between a convection-resolving nested

domain with 4-km grid spacing and a parent domain with cumulus parameterization and 36-km grid spacing.

Simulations using 4-km grid spacing are the most intense, with the maximum intensity falling close to

empirical estimates of maximum TC intensity. Sensitivity to SL and PBL parameterization also exists, most

notably in simulations with 4-km grid spacing, where the maximum intensity varied by up to ;10 m s21

(V10max) or ;13 hPa (Pmin). Values of surface latent heat flux (LHFLX) are larger in MYJ than in YSU at the

same wind speeds, and the differences increase with wind speed, approaching 1000 W m22 at wind speeds in

excess of 55 m s21. This difference was traced to a larger exchange coefficient for moisture, CQ, in the MYJ

scheme. The exchange coefficients for sensible heat (Cu) and momentum (CD) varied by ,7% between the

SL schemes at the same wind speeds. The ratio Cu/CD varied by ,5% between the schemes, whereas CQ/CD

was up to 100% larger in MYJ, and the latter is theorized to contribute to the differences in simulated

maximum intensity. Differences in PBL scheme mixing also likely played a role in the model sensitivity.

Observations of the exchange coefficients, published elsewhere and limited to wind speeds ,30 m s21,

suggest that CQ is too large in the MYJ SL scheme, whereas YSU incorporates values more consistent

with observations. The exchange coefficient for momentum increases linearly with wind speed in both

schemes, whereas observations suggest that the value of CD becomes quasi-steady beyond some critical wind

speed (;30 m s21).

1. Introduction

It has been shown that improvements in the accuracy

of tropical cyclone (TC) intensity predictions continue

to lag improvements in track prediction (e.g., Knaff

et al. 2003; DeMaria et al. 2005; Rogers et al. 2006). This

discrepancy is in part due to the fact that numerical

models are able to provide reliable track guidance even

when the intensity forecast from the same model is in-

accurate, provided that the synoptic-scale steering flow

is reasonably well depicted. The lack of accuracy in

numerical intensity forecasts from operational dynami-

cal models is attributable to several factors, including

but not limited to (i) poor representation of TCs in

model initial conditions (e.g., Kurihara et al. 1995, 1998;

Xiao et al. 2000; Zou and Xiao 2000; Aberson 2003), (ii)

inaccuracies in model representation of processes tak-

ing place near the air–sea interface (e.g., Emanuel 1995;

Andreas and Emanuel 2001; Braun and Tao 2000; Per-

rie et al. 2005), and (iii) model resolution (e.g., Braun

and Tao 2000; Davis and Bosart 2002; Persing and

Montgomery 2003). The resolution sensitivity is linked

to a growing body of evidence that small-scale vortices

in and near the eyewall can alter TC thermodynamics

sufficiently to change intensity (e.g., Persing and Mont-

gomery 2003; Braun et al. 2006; Gentry 2007; Cram et

al. 2007; Yang et al. 2007). In this study, we will use the

Weather Research and Forecasting Advanced Research

Model (WRF-ARW) to examine factors ii and iii above,

Corresponding author address: Kevin A. Hill, Department of

Marine, Earth and Atmospheric Sciences, North Carolina State

University, 1125 Jordan Hall, Raleigh, NC 27695-8208.

E-mail: [email protected]

FEBRUARY 2009 H I L L A N D L A C K M A N N 745

DOI: 10.1175/2008MWR2220.1

� 2009 American Meteorological Society

while eliminating consideration of i by utilizing ideal-

ized simulations of long duration.

Tropical cyclones intensify and maintain themselves

against dissipation by extracting energy from the ocean

(e.g., Byers 1944; Emanuel 1986); therefore numerical

model simulations of TCs are highly sensitive to the

parameterization of energy transfer processes at the

air–sea interface (e.g., Ooyama 1969). Numerical mod-

els calculate the air–sea exchange of heat, moisture, and

momentum using a surface layer (SL) parameterization

scheme, and estimate turbulence-induced tendencies of

momentum and thermodynamic quantities using a

planetary boundary layer (PBL) scheme. The validity

of current model SL parameterizations in TC environ-

ments is questionable, owing to their empirical nature

and the lack of observational data taken at high wind

speeds over water (e.g., Large and Pond 1981; Emanuel

1995; Braun and Tao 2000; Powell et al. 2003; Perrie et

al. 2005). Recent field observations, such as those taken

during the Coupled Boundary Layers/Air–Sea Transfer

(CBLAST) experiment (Black 2004; Black et al. 2007),

suggest that linear extrapolation of exchange coeffi-

cients from those based on low wind speed measure-

ments, as done in current SL schemes, is incorrect. PBL

parameterization schemes also impact simulated TC in-

tensity, but typically to a lesser extent than SL schemes

(Braun and Tao 2000). To assess simulated TC sensi-

tivity to these parameterizations, several previous stud-

ies have performed numerical simulations of real-case

TCs and compared the results with observations (e.g.,

Braun and Tao 2000; Davis and Bosart 2002). Through

this comparison, the model’s ability to accurately rep-

resent a TC can be assessed, and, indirectly the validity

of model design assumptions can be investigated.

In addition to turbulence parameterization, it is rec-

ognized that TC simulations are sensitive to other pa-

rameterizations as well, such as precipitation micro-

physics (e.g., Rogers et al. 2007), and subgrid-scale cu-

mulus convection (e.g., Ooyama 1982; Karymampudi et

al. 1998). While we recognize these sensitivities, our

emphasis here is upon the turbulence parameterization,

and in particular the surface flux parameterization.

In addition to these parameterization issues, TC

simulations are also sensitive to horizontal and vertical

resolution (e.g., Braun and Tao 2000; Davis and Bosart

2002; Persing and Montgomery 2003; Zhang and Wang

2003; Kimball and Dougherty 2006), since altering the

grid spacing influences how well different physical pro-

cesses are resolved, and impacts the behavior of param-

eterization schemes. Braun and Tao (2000) found that

smaller horizontal grid spacing led to more intense

modeled TCs. However, Davis and Bosart (2002) found

that simulations of Hurricane Diana (1984) were more

intense on a 9-km grid than on a 3-km grid because of

a distribution of vertical motion on the 9-km grid that

was skewed toward updrafts, increasing vorticity gen-

eration through stretching. Higher-resolution simula-

tions have also been shown to resolve mixing between

the low-level eye and the eyewall, which provides extra

buoyancy to eyewall updrafts, leading to more intense

simulated TCs (e.g., Persing and Montgomery 2003; Wu

et al. 2006; Montgomery et al. 2006; Cram et al. 2007).

This study aims to quantify the sensitivity of simu-

lated TCs to SL and PBL representation and model

grid spacing through the use of idealized simulations. In

contrast to many previous studies, we will utilize ideal-

ized simulations of long duration. The use of idealized

conditions conducive to intense TC development allows

for model results to be viewed in the absence of case-

specific conditions. A comparison between model results

and observationally based empirical estimates of maxi-

mum potential intensity (MPI) is presented and is used as

a benchmark for model performance in the place of ob-

servations. This comparison is a necessary prerequisite

to a more complete implementation of high wind speed

exchange coefficients in NWP models. Flux and ex-

change coefficient values are compared for two widely

used SL schemes, and the results are discussed in light

of recent observational measurements.

In section 2, the numerical experiments are de-

scribed, including the idealized initial and boundary

condition dataset, the methods used to estimate MPI,

and other model configurations. Section 3 provides a

description of the TC intensity found in each simula-

tion, and a comparison of the results to the empirically

estimated maximum intensity. Section 4 describes the

sensitivity of model surface fluxes to the SL parameter-

ization scheme, and conclusions are presented in sec-

tion 5.

2. Simulation description

a. Model

Version 2.1.21 of the WRF-ARW model (Skamarock

et al. 2005) was used to conduct two separate sets of

model experiments designed to test the sensitivity to

model physics and grid spacing (Table 1), with each set

utilizing either the Yonsei University (YSU) or the

Mellor–Yamada–Janjic (MYJ) suite of PBL and SL pa-

rameterizations. WRF version 2.1.2 must be run with

PBL and SL schemes as a matching pair, precluding the

ability to test SL or PBL schemes individually. Higher-

1 Results obtained from version 2.2 are consistent with those

presented here.

746 M O N T H L Y W E A T H E R R E V I E W VOLUME 137

resolution simulations were performed using one-way

interactive nests between the coarse grid (36-km grid

spacing) and two finer grids (12 and 4 km). Both the 12-

and 4-km grids were moved using an automatic vortex-

tracking algorithm to keep the storm nearly centered in

the nested domains; despite a lack of environmental

flow in the idealized model environment, beta drift gen-

erates a west-northwest movement of the simulated

TCs. The model simulations utilized 31 vertical layers,

with a higher concentration located in the boundary

layer.

The Kain–Fritsch cumulus parameterization scheme

(Kain and Fritsch 1993; Kain 2004) was used to estimate

the effects of subgrid-scale convection on the 12- and

36-km grids, while cumulus convection was not param-

eterized on the 4-km grids. The top of the model atmo-

sphere was set at the 50-hPa pressure level, with a Ray-

leigh damping layer used near the model top in order to

prevent the reflection of wave energy back into the

model domain. The Purdue–Lin scheme was used for

the parameterization of microphysical processes (Lin et

al. 1983; Hong et al. 2004). The Rapid Radiative Trans-

fer Model (RRTM) scheme, based on Mlawer et al.

(1997) and adapted from the fifth-generation Pennsyl-

vania State University–National Center for Atmo-

spheric Research (PSU–NCAR) Mesoscale Model

(MM5), was used to estimate the effects of longwave

radiation. Shortwave radiation was represented using

the scheme described by Dudhia (1989).

The SL schemes compute roughness length, friction

velocities, exchange coefficients, and surface fluxes.

The SL parameterization scheme compatible with the

YSU PBL scheme is based on Monin–Obukhov simi-

larity theory (Monin and Obukhov 1954), with several

modifications. Surface exchange coefficients for heat,

moisture, and momentum are estimated using stability

functions from Paulson (1970), Dyer and Hicks (1970),

and Webb (1970). The YSU SL scheme classifies the

surface layer as being representative of one of four sta-

bility regimes as discussed by Zhang and Anthes

(1982), which are determined by the Bulk Richardson

number (BR). The MYJ SL scheme (Janji�c 1996, 2002;

Z. I. Janji�c 1998, personal communication) is also based

on Monin–Obukhov similarity theory. Using an itera-

tive approach, first-guess momentum and heat flux val-

ues are used to estimate the Obukhov length. The it-

erative procedure typically converges after three or less

iterations (Z. I. Janji�c 1998, personal communication).

Tendencies of basic variables due to turbulent eddies

are computed by the model PBL scheme. Using values

of surface fluxes calculated by the SL scheme, the PBL

scheme estimates flux distributions within the boundary

layer, providing tendencies of temperature, moisture,

and horizontal momentum. The YSU PBL scheme

(Noh et al. 2003; Hong et al. 2006) is a successor to the

MRF PBL scheme (Hong and Pan 1996), and estimates

fluxes due to nonlocal gradients using countergradient

terms. New to the YSU scheme is an explicit treatment

of the entrainment at the PBL top, which was found to

significantly improve model results (Noh et al. 2003;

Hong et al. 2006). The PBL top is defined using a criti-

cal BR number of zero, and is generally lower than in

the MRF scheme. The MYJ PBL parameterization is

based on Mellor–Yamada 2.5-level turbulence closure.

The PBL height in this scheme is defined based on

turbulent kinetic energy (TKE). The vertical limit over

which mixing can occur in this scheme is proportional

to the TKE and a function of large-scale buoyancy and

shear parameters (Janji�c 2002).

b. Environment and initial conditions

Model runs were initialized with an idealized tropical

environment designed to allow for the development of

strong TCs. The idealized initial conditions were used

to initialize the full-physics WRF Model on an actual

geophysical domain, but with the domain set to include

only water. Tropical cyclones in the real atmosphere

rarely attain their MPI, often because of the limiting

effects of wind shear and upwelling (e.g., DeMaria and

Kaplan 1994, hereinafter DK94; Tonkin et al. 2000), in-

teractions with land, and dry environmental air. To pro-

vide atmospheric conditions within which a TC should

reach its MPI, a model domain consisting of all water

was constructed with (i) a horizontally uniform, time-

independent SST of 298C, (ii) no environmental wind

shear, and (iii) a constant environmental relative hu-

TABLE 1. List of simulation names for idealized simulations.

Simulation name PBL/SFC physics Cumulus parameterization Grid spacing (km) Grid dimension Vertical levels

MYJ36 MYJ Kain–Fritsch 36 99 3 104 31

MYJ12 MYJ Kain–Fritsch 12 111 3 111 31

MYJ4 MYJ None 4 246 3 246 31

YSU36 YSU Kain–Fritsch 36 99 3 104 31

YSU12 YSU Kain–Fritsch 12 111 3 111 31

YSU4 YSU None 4 246 3 246 31


midity of 80%. The ambient temperature profile (and

lateral boundary condition for the outermost domain)

was specified by the mean tropical sounding of Jordan

(1958), within which a weak initial vortex (i.e., maxi-

mum near-surface wind speeds of ;22 m s21 and mini-

mum central pressure of ;990 hPa) in hydrostatic and

gradient wind balance was inserted. Model simulations

were performed with a wide variety of idealized vorti-

ces, ranging from an unbalanced warm bubble to fully

balanced vortices. The most important difference be-

tween these runs was the amount of time required for

the system to reach maximum intensity; an initial vor-

tex strength of 22 m s21 was used in order to reduce the

amount of time needed to reach the maximum inten-

sity, while not overprescribing the system structure.

These findings, which are consistent with previous ide-

alized modeling studies (e.g., Ooyama 1969; Rosenthal

1971), are not presented here in the interest of brevity.

In this case, an integration length of 10 days allowed for

the simulated TCs to attain a quasi-steady maximum

intensity and then begin weakening. Experiments with

varying run length confirm that 10 days is adequate for

the purposes of this study.

c. MPI comparisons

DK94, utilizing a 31-yr sample of tropical cyclones in

the North Atlantic basin, developed an empirical rela-

tionship between climatological sea surface tempera-

ture (SST) and TC maximum intensity. The results

were shown to agree with the theoretical MPI formu-

lation of Emanuel (1988). The observationally based

empirical formulation for MPI of DK94 will provide the

basis for a comparison to the model runs; a SST of 298C

predicts maximum sustained 10-m winds (V10max) of

;75 m s21. DK94 do not provide an estimate of mini-

mum central pressure (Pmin), but a V10max of 75 m s21

corresponds to a Pmin value of 910 hPa using the pres-

sure–wind relationship of Brown et al. (2006), or 891

using the relation of Atkinson and Holliday (1977). The

difference in the relationship between Pmin and V10max

in these two studies is likely due to the observational

datasets used to determine the relationship; the Atkin-

son and Holliday (1977) study utilized a dataset con-

sisting of Pacific TCs, while Brown et al. (2006) utilized

data from Atlantic TCs. Since the idealized initial vor-

tex is not necessarily intended to represent either ocean

basin, simulated MSLP values will be compared to both

estimates.

3. Intensity

To determine a 10-m wind speed value from the

model output, an assumption regarding the wind speed

profile in the boundary layer is required, since the low-

est model layer is above 10 m. For consistency with the

observationally determined estimates of maximum

10-m wind speed used in DK94, 10-m wind speed was

obtained by multiplying the model wind speed at the

700-hPa level by 0.90 [based upon the recommendation

of Franklin et al. (2000) and used in DK94]. Sampling

issues exist when comparing model results to observa-

tions, since the maximum intensity of an observed TC

may not always be sampled sufficiently. This issue must

be taken into account when comparing the results of the

model simulations with the observationally based MPI

estimates of DK94.

Figure 1 shows a time series of the model-simulated

V10max for the duration of the 240-h simulations. In each

simulation, the storm undergoes a period of rapid in-

tensification during the first 24 h of model integration,

reaching hurricane strength (;33 m s21) within 12 h.

Simulations using 4- or 12-km grid spacing intensify at

nearly the same rate through 24 h, but after this time

maximum winds level off in the 12-km simulations,

while continuing to increase in the 4-km simulations.

After hour 72, V10max is quasi-steady (610 m s21) in all

simulations except YSU4, where an increase in the TC

size after simulation hour 120 led to a weaker pressure

gradient (not shown) and weaker V10max (Fig. 1b).

Simulations with higher resolution produce stronger

winds, and the MYJ4 and YSU4 simulations both ex-

ceed the estimated MPI of 75 m s21; however, the dif-

ference of ;5 m s21 in the YSU4 run is quite small,

given the assumptions used in our 10-m wind compu-

tation and uncertainty in the observations that were

used to derive this empirical MPI. Simulations with 12-

km grid spacing produce peak V10max values that are

near (,5 m s21 difference) the MPI, while the 36-km

grid spacing simulations are 5–10 m s21 below the

MPI.2

Figure 2 shows a time series of the model-simulated

Pmin. The evolution of Pmin is similar to that of V10max,

with rapid deepening in the first 24 h of each simula-

tion, varying amounts of intensification between 24 and

144 h depending upon the specific simulation, and then

quasi-steady Pmin after hour 144. The 4-km simulations

produce TCs with the lowest Pmin values, yielding pres-

sures slightly lower than those provided by either of

the pressure–wind relationships described above. The

TC in simulation YSU12 attains a minimum central

2 We acknowledge that the comparison between maximum

wind speed values between model domains with different grid

spacings is not direct, as smaller grid boxes more easily attain a

given maximum speed than larger grid boxes. However, the result

of higher intensity in the higher-resolution runs was also evident

with all data interpolated to a 36-km grid (not shown).


pressure of 900 hPa, a value that falls between the Pmin

estimates discussed above. Simulations MYJ12,

YSU36, and MYJ36 all reach a similar Pmin of ;910–

915, within ;5 hPa of the estimate based on Brown et

al. (2006). The sensitivity of Pmin to parameterization

choice varies with grid spacing, with simulations utiliz-

ing the MYJ parameterizations and 4 (12) km grid spac-

ing being more (less) intense than those with YSU.

Simulations with 36-km grid spacing were of compa-

rable intensity with the two schemes. We speculate that

the use of a convective parameterization (CP) scheme

in the 12- and 36-km simulations could contribute to

this discrepancy; CP scheme activity in the eyewall re-

duces the TC secondary circulation, and the interplay

between shallow mixing in the CP scheme and param-

eterized moist entrainment in the YSU scheme may

explain the differences between runs with explicit and

parameterized convection. Additional simulations

would be required to determine whether TCs in MYJ

simulations would be consistently stronger than for the

YSU scheme, but this was the case for all of the explicit

convection runs that we performed.

FIG. 1. Time series of model maximum 10-m wind speed (m s21; model run indicated in

legend) for the (a) MYJ and (b) YSU simulations.


The fact that in the simulations using 4-km grid spac-

ing Pmin values showed little sensitivity to parameter-

ization choice, while V10max values did, is likely due to

differences in the simulated TC size. After simulation

hour 120, the simulated TC in YSU4 grew to be much

larger than in MYJ4. Therefore, despite a continued

deepening of the vortex, the maximum V10max values in

YSU4 are found before simulation hour 120, while the

lowest Pmin occurs close to simulation hour 200. The

sensitivity of model-simulated TC size to the surface

layer and planetary boundary layer parameterization

schemes is the topic of ongoing research.

4. Sensitivity of fluxes and exchange coefficients toSL parameterization

Since theory and previous modeling studies have in-

dicated a relationship between hurricane intensity and

the model turbulent exchange coefficients (Ooyama

1969; Rosenthal 1971; Emanuel 1995; Braun and Tao

2000), it is anticipated that different exchange coeffi-

FIG. 2. Time series of model minimum central pressure (hPa; model run indicated in

legend) for the (a) MYJ and (b) YSU simulations.


cients (and fluxes) computed by the WRF SL param-

eterization schemes tested here will contribute sub-

stantially to the differences in simulated TC intensity.

Because the SL characteristics may vary in each simu-

lation because of factors other than the SL parameter-

ization (such as the different PBL schemes being used),

it can be difficult to evaluate the SL schemes unless

identical winds, temperatures, and vapor mixing ratios

are used in the calculations. To alleviate this difficulty,

the values of different SL parameters from the 4-km

grid spacing simulations will be presented as a function

of the 10-m wind speed. The model output 10-m wind

speed is much less than the 10-m wind speed we esti-

mate utilizing from multiplying the 700-hPa wind speed

by 0.9, but it is used for analyzing the surface layer

parameters because it is the wind speed used by the

schemes for the calculations. Output from simulation

hour 102 will be shown, since the TCs exhibited similar

near-surface wind speeds at this time (Fig. 3). Exami-

nation of other times demonstrates that the results are

not sensitive to this choice. To examine the average

conditions near the TC center, 280-km area-averaged

(hereafter AA) fields will be discussed. The 280-km

distance was chosen because it allows for the core of

strong winds to be covered, although the results are not

highly sensitive to this choice. The AA 10-m wind

speed (V10) is nearly identical between the two 4-km

runs at this simulation hour, allowing for a consistent

comparison between area-averaged SL parameters

(Table 2).

Figure 4 displays latent heat flux (LHFLX) as a func-

tion of 10-m wind speed. Values of LHFLX are larger

in MYJ4 than in YSU4 at wind speeds stronger than

;17 m s21, with the largest differences, up to 1000 W

m22, found at wind speeds above 55 m s21. The AA

10-m wind speeds vary by ;1 m s21 between the runs,

yet the AA LHFLX is 178 W m22 (;22%) larger in the

MYJ4 simulation (Table 2). The large disparity in the

LHFLX values could be due to different vertical mois-

ture gradients near the ocean surface in the simulations,

or due to other differences within the SL schemes. To

investigate these possibilities, the difference in specific

humidity between the surface and 10 m was calculated

(hereinafter referred to as Dq0–10). All else being equal,

the moisture flux should be larger in a simulation in

which the vertical water vapor gradient near the ocean

surface is larger. However, Fig. 5 reveals that the near-

surface vertical moisture gradient is larger in the YSU4

simulation relative to MYJ4 at all wind speeds shown.

At high wind speeds, where LHFLX values are ;50%

larger in MYJ4, Dq0–10 remains larger in the YSU4

simulation. These results suggest that the significant

differences in the LHFLX between the schemes is re-

lated to the moisture exchange coefficient, CQ (see the

Appendix for the computational method), which is

shown in Fig. 6 as a function of wind speed. In MYJ4,

CQ linearly increases with wind speed, while in YSU4

CQ is nearly constant with wind speed. At wind speeds

of 50 m s21 and above, the CQ value in the MYJ4 simu-

lation is more than twice as large as in YSU4, and over-

all the AA CQ value is ;50% larger in MYJ4 (Table 2).

To summarize, AA LHFLX values are 22% larger in

the MYJ4 simulation despite having a smaller gradient

of moisture near the surface, because of a larger ex-

change coefficient for moisture.

While there are large differences in LHFLX values

produced in the simulations, the values of sensible heat

flux (HFLX) are more similar (Fig. 7). Values of HFLX

differ by up to ;50 W m22. The AA HFLX values are

;30% larger in the MYJ4 simulation (Table 2), but this

difference can be mainly attributed to the distribution

of potential temperature (u) in the SL. The near-

surface vertical u gradient is larger in the MYJ4 simu-

lation at almost all wind speeds (Fig. 8), leading to an

AA vertical u gradient that is ;27% larger (Table 2).

The values of the exchange coefficient for sensible heat,

Cu, used in the schemes are within 5% of one another at

all wind speeds shown (Fig. 9) and AA values vary by

,3% (Table 2), supporting the fact that the calculation

of HFLX is nearly identical in the MYJ and YSU SL

schemes. Examination of Table 2 reveals that the ex-

change coefficients for moisture and heat are identical

in the MYJ4 simulation, but are not in YSU4.

Figure 10 is a plot of the momentum exchange coef-

ficient, CD, as a function of 10-m wind speed. Through-

out the range of winds speeds shown, CD is nearly iden-

tical in the two model simulations, indicating that dif-

ferences in this parameter likely did not play a role in

the sensitivity to the surface layer parameterization.

Emanuel (1995), utilizing an idealized hurricane

model, investigated the sensitivity of simulated TC in-

tensity to the ratio Ck (the exchange coefficient for

enthalpy) to CD. The results suggested that the value in

real hurricanes is likely between 0.75 and 1.5. As pre-

viously shown, the exchange coefficients for heat and

water vapor are equal in the MYJ SL scheme, but not

in the YSU scheme. Therefore, the ratios Cu/CD and

CQ/CD will each be examined separately. At almost all

wind speeds, Cu/CD is larger in the MYJ4 simulation

(Fig. 11), although the largest difference is ;3%, and

AA values are within 1% of one another (Table 2).

Values at all wind speeds fall within the range sug-

gested by Emanuel (1995). The ,1% difference in the

AA Cu/CD value is not likely to fully explain the ob-

served difference in intensity. Figure 12 displays the

value of the ratio CQ/CD. Owing to the fact that CQ


increases more slowly with wind speed than CD in the

YSU4 simulation, the ratio CQ/CD decreases with in-

creasing wind speed. The largest difference in CQ/CD is

at wind speeds greater than 50 m s21, where CQ/CD is

approximately twice as large in the MYJ4 simulation.

The AA values of the ratio are ;55% larger the MYJ4

simulation. At wind speeds above ;35 m s21, the ratio

in the YSU4 simulation is less than the minimum value

suggested by Emanuel (1995), although it is difficult to

assess the realism of this behavior due to a lack of flux

observations at high wind speeds over water. We specu-

late that the large difference in this ratio is most likely

responsible for the differences in simulated TC inten-

sity seen in the MYJ4 and YSU4 simulations.

FIG. 3. Model 10-m wind speed (shaded; m s21) at simulation hour 102 for the (a) MYJ and

(b) YSU simulations. The black contour indicates the 280-km distance from the TC centers.


5. PBL tendencies

The impact of PBL parameterization on the vertical

structure of the simulated TCs was assessed by exam-

ining vertical cross sections of temporally and azimuth-

ally averaged potential temperature and mixing ratio,

along with tendencies of temperature and moisture due

to PBL parameterization. Hourly model output from

the 4-km grid spacing simulations during the period

from 72 to 84 h was used. In cases where negative and

positive tendencies were both present, the tendencies

were averaged separately, to avoid cancellation.

Figure 13 displays the average potential temperature

from the 4-km simulations for this 12-h interval. A re-

alistic warm-core structure is evident in both simula-

tions (Figs. 13a,b), although the TC core is generally

warmer in the MYJ4 simulation than in YSU4 (Fig.

13c). The largest difference (;8 K) is found between 4-

and 6-km altitude within ;35 km of the TC center. The

difference in potential temperature in this area can be

partially attributed to PBL scheme tendencies of heat

(Fig. 14). The YSU PBL scheme produced strong (;10

K h21) cooling in this area (Fig. 14b), while the MYJ

PBL scheme produced no tendency (Fig. 14a).

Outside of the eye, large differences in the magni-

tude and location of PBL scheme potential temperature

tendency exist as well. Azimuthally and temporally av-

eraged positive (warming) tendencies are up to ;8 K in

both schemes, while the maximum cooling is approxi-

mately one order of magnitude larger in the YSU

scheme. The YSU scheme produces appreciable ten-

dencies up to ;8-km altitude, while the MYJ scheme

FIG. 4. Model latent heat flux (W m22) as a function of 10-m wind speed (simulation

indicated in legend) at simulation hour 102.

TABLE 2. Model 10-m wind speed, surface latent heat flux (LHFLX), the difference in specific humidity between the surface and the

10-m level (Dq0–10), sensible heat flux (HFLX), the difference in potential temperature between the surface and the 10-m level (Du0–10),

the exchange coefficient for moisture (CQ), heat (Cu) and momentum (CD), and the ratios Cu/CD and CQ/CD. For each simulation, the

first number in the column is the average value within 280 km of the storm and the second and third numbers are the minimum and

maximum within that area. Values are from simulation hour 102.

Case

10-m wind

(m s21)

LHFLX

(W m22)

Dq0–10

(g kg21)

HFLX

(W m22) Du0–10 (K) CQ (3 1023) Cu (3 1023) CD (3 1023) Cu/CD CQ/CD

MYJ4 27.58 971 2.41 133 1.28 2.30 2.30 2.60 0.89 0.89

1.31 26 1.34 4 0.45 1.30 1.30 0.90 0.80 0.80

60.22 3455 3.06 840 4.40 4.13 4.13 4.92 1.46 1.46

YSU4 28.51 793 2.40 103 0.88 1.09 2.35 2.65 0.89 0.58

0.78 13 1.56 1 0.21 0.95 1.12 1.11 0.85 0.40

58.18 2014 3.07 642 3.86 1.90 4.08 4.80 1.03 1.01


generally produces a shallower layer of heating and

cooling, up to ;5-km altitude.

Figure 15 displays the average mixing ratio from the

4-km simulations, with an outward-sloping eyewall seen

in both simulations (Figs. 15a,b). The largest difference

in mixing ratio is found in the TC center, where the

MYJ4 simulation is dryer than in YSU4 by up to ;4 g

kg21 (Fig. 15c). The difference in mixing ratio in the

aforementioned area can be partially attributed to PBL

scheme tendencies of moisture (Fig. 16). The YSU PBL

scheme produced strong (.4.5 g kg21) moistening in

this area (Fig. 16b), while the MYJ PBL scheme pro-

FIG. 5. The difference in mixing ratio (g kg21) between the surface and the 10-m level, as a

function of 10-m wind speed (simulation indicated in legend).

FIG. 6. The exchange coefficient for moisture, CQ (3 1023), as a function of 10-m wind

speed (simulation indicated in legend).


duced no tendency (Fig. 16a). Outside of the eye, the

PBL schemes in general produce a similar pattern of

mixing. The YSU scheme produces negative (drying)

tendencies that are up to 10 times larger than in MYJ.

6. Discussion and conclusions

The WRF model has been used to produce idealized

TC simulations within an environment that allows for

intensification to the environmental MPI of the model

atmosphere. The empirical relationship between SST

and maximum intensity of DK94 provides a comparison

that is useful in determining the overall consistency of

the model with observations, although it is important to

emphasize that numerous complexities exist when com-

paring observations to model output and the intensity

comparison is more qualitative than quantitative in na-

FIG. 7. Model sensible heat flux (W m22) as a function of 10-m wind speed (simulation

indicated in legend).

FIG. 8. The difference in potential temperature between the surface and the 10-m level (K)

as a function of 10-m wind speed (simulation indicated in legend).


ture. More specifically, the sensitivity to model resolu-

tion and SL and PBL physics was investigated by per-

forming two separate experiments, where the horizon-

tal grid spacing was varied on three domains. Much of

the model sensitivity is attributed to the SL physics,

although large differences in PBL scheme–induced

mixing have been shown to exist, and could impact the

simulated TC intensity as well. Additional sensitivity of

the results to microphysics parameterization, the use of

convective parameterization on the outer grids, or

other aspects of the model have not been systematically

addressed here.

FIG. 9. The exchange coefficient for sensible heat, Cu (3 1023), as a function of 10-m wind


FIG. 10. The momentum exchange coefficient, CD (3 1023), as a function of 10-m wind



a. Maximum TC intensity

The maximum intensity reached in the simulations

exhibited strong sensitivity to horizontal grid spacing,

and to a lesser extent to the choice of SL and PBL

parameterization. Simulations using 4-km grid spacing

produced TCs that were of comparable intensity to em-

pirical MPI estimates for the idealized environment,

while simulations using coarser (12 or 36 km) grid spac-

ing were weaker. The greater intensity seen in the

higher-resolution domains is likely due to either (i) the

omission of convective parameterization on the 4-km

grid, and/or (ii) the ability of the higher-resolution do-

main being able to at least partially resolve mixing by

FIG. 11. The ratio of the exchange coefficient for heat to the exchange coefficient

momentum (Cu /CD) as a function of 10-m wind speed (simulation indicated in legend).

FIG. 12. The ratio of the exchange coefficient for moisture to the exchange coefficient for

momentum (CQ /CD) as a function of 10-m wind speed (simulation indicated in legend).


FIG. 13. Temporally and azimuthally averaged potential temperature (K)

for the (a) MYJ4, (b) YSU4, and (c) MYJ4 – YSU4 simulations.


eyewall vortices between the low-level eye and the eye-

wall; these findings are thus consistent to those of Pers-

ing and Montgomery (2003), Braun et al. (2006), and

Cram et al. (2007). Simulations utilizing sub 4 km have

not been tested here, but we speculate that simulations

with even higher resolution would be more intense

(Montgomery et al. 2006; Gentry 2007).

b. Fluxes and exchange coefficients in the YSU andMYJ schemes

Large differences are shown to exist between LH-

FLX computations between the two available surface

layer parameterization schemes in WRF. The MYJ

scheme produces values of LHFLX that are up to 1000

FIG. 14. Temporally and azimuthally averaged PBL potential temperature tendency (K

h21). Positive (negative) values are shaded (contoured) for the (a) MYJ4 and (b) YSU4

simulations. Note that positive and negative tendencies are contoured at different intervals,

and the negative tendencies are contoured at different intervals between the schemes.


FIG. 15. Temporally and azimuthally averaged mixing ratio (g kg21) for

the (a) MYJ4, (b) YSU4, and (c) YSU4 – MYJ4 simulations.


W m22 (;50%) larger than those in the YSU scheme at

the same wind speeds. This was traced to a larger ex-

change coefficient for moisture (CQ) in the MYJ

scheme. The CQ in the YSU scheme is nearly indepen-

dent of wind speed (varying between 1.4 and 1.8), while

in the MYJ scheme CQ linearly increases with wind

speed, reaching a value of ;3.8 3 1023 at a wind speed

of ;55 m s21. The difference in the LHFLX values

calculated by the schemes increases with increasing

wind speed, suggesting that the sensitivity of TC inten-

sity to the parameterization scheme may be largest for

intense systems. The large values of LHFLX at high

wind speeds due to the large CQ value may have been

the factor that allowed the MYJ4 simulation to exceed

FIG. 16. Temporally and azimuthally averaged PBL water vapor tendency (g kg21 h21).

Positive (negative) values are shaded (contoured) for the (a) MYJ4 and (b) YSU4 simulations.

Note that negative tendencies in the MYJ4 simulation are multiplied by 10, and that the

contour interval of the negative and positive tendencies is different.


the intensity of YSU4. Values of HFLX and the ex-

change coefficients for momentum and heat are nearly

identical in the MYJ and YSU schemes.

c. Comparison with observations

Assessing which scheme is more realistic is compli-

cated by the lack of observations at high wind speeds

over oceans. Numerous studies have attempted to esti-

mate the turbulent exchange coefficients over water in

high wind speed conditions (e.g., Smith 1980; Large and

Pond 1981; Smith et al. 1992; Yelland et al.1998; Powell

et al.2003) utilizing a wide range of measurement plat-

forms and analysis techniques. Measurements during

the 2002–04 Coupled Boundary Layers Air–Sea Trans-

fer (CBLAST) field program were made at wind speeds

up to ;28 m s21, allowing for the exchange coefficients

to be estimated based on measurements at higher wind

speeds than was previously possible. Model-simulated

wind speeds greatly exceeded these values, but never-

theless, CBLAST observations provide the best metric

for assessing the surface layer parameterization

schemes over the widest range of wind speeds possible.

CBLAST observations indicate that CD is quasi-steady

at wind speeds within the range of ;18–28 m s21 (Black

et al. 2007, their Fig. 5), with a value of 1.5–2.0. At wind

speeds in this range, CD is nearly identical in the MYJ

and YSU SL schemes, with a value of ;2.1–2.6 3 1023,

exceeding the upper bound of the observations. At

wind speeds . 30 m s21, CD increases with wind speed

in both model SL schemes, reaching a value of ;4.6 3

1023 at a wind speed of ;55 m s21. Based on the avail-

able observations, it is evident that the momentum ex-

change coefficient may be too large in both the YSU

and MYJ schemes.

CBLAST observations indicate that the exchange co-

efficient for moisture is quasi-steady with increasing

wind speed for wind speeds ,28 m s21. The CQ in-

creases slowly with wind speed in the YSU scheme,

while in MYJ it increases more rapidly with increasing

wind speed. At wind speeds ,28 m s21, CQ in the YSU

scheme more closely matches the observations. At a

wind speed of ;28 m s21, the CQ value from the MYJ

scheme exceeding the upper bound of the observations,

suggesting that the scheme overestimates CQ, and con-

sequently LHFLX. The wind speed dependence of CQ

in higher wind speed conditions (.;30 m s21) is diffi-

cult to assess given the limited range of observational

data, although it is clear that the MYJ scheme produces

much larger values than YSU.

Previous modeling studies and theoretical work sug-

gest that the ratio of the exchange coefficient for en-

thalpy to the exchange coefficient for momentum

strongly influences simulated TC intensity. Here it is

suggested that when Cu 6¼ CQ, the ratios Cu/CD and

CQ/CD can both impact simulated TC intensity, and,

given the fact that latent heat fluxes are much larger

than sensible, CQ/CD may ultimately be more impor-

tant. Theory suggests that increasing (decreasing) these

ratios should lead to a more (less) intense simulated

TC, and that the ratio should be between 0.75 and 1.5

(e.g., Emanuel 1995). Observations, although limited to

wind speeds ,30 m s21, indicate that the ratio may be

toward the lower end of that spectrum, with a value of

;0.75 (Black et al. 2007, their Fig. 7). Recent modeling

studies suggest that full-physics numerical models can

produce TCs of realistic intensity while utilizing values

of this ratio of ,0.75 (Cram et al. 2007). The ratio

Cu/CD is similar in the MYJ4 and YSU4 simulations,

with values between 0.8 and 0.95, in good agreement

with Emanuel (1995) and slightly larger than that indi-

cated by CBLAST observations (but within the range

of uncertainty in the measurements). The small differ-

ences in this ratio likely do not contribute to differences

in model TC intensity.

The ratio CQ/CD varies significantly between the

schemes; in the MYJ4 simulation the value is between

0.8 and 0.95, while in YSU4 the ratio decreases from

;0.75 to 0.40 as wind speed increases from 20 to 55

m s21. This ratio is less than that suggested by Emanuel

(1995), although this does not necessarily indicate a

problem, as the model is still capable of producing re-

alistic TC intensity. The value in YSU4 at a wind speed

of 30 m s21 falls within the 95% confidence interval of

the CBLAST observations, but the decrease at higher

wind speeds cannot be assessed using currently avail-

able observations. The smaller ratio at high wind

speeds should lead to less intense TCs in YSU than in

simulations with the MYJ SL scheme. Owing to the fact

that the ratio becomes more dissimilar at higher wind

speeds, it is anticipated that simulations of weaker TCs

would exhibit less sensitivity to SL parameterization.

The results presented here are consistent in this regard,

as modeled TC intensity using 36-km grid spacing was

similar (,1 m s21 difference in peak V10max), whereas

TC intensity using 4-km grid spacing varied consider-

ably (;10 m s21 difference in peak V10max).

d. Implications for TC modeling

Based upon the observational data it is evident that a

linear extrapolation of measured exchange coefficient

values at low wind speeds, as is done in the MYJ and

YSU schemes, may not yield physically realistic ex-

change coefficient values in the high wind speed con-

ditions of an intense TC. Despite this apparent incon-


sistency between the model values and observations,

and even for an extremely intense TC, WRF-ARW is

capable of producing simulated TC intensity that is

comparable to empirical estimates of maximum inten-

sity. It is unclear what effect modifying the model ex-

change coefficients in the model would produce, al-

though theory suggests that if both CD and CQ (or Cu)

were changed in the same sense then the simulated TC

intensity should not change. Changes that lead to the

ratio increasing (decreasing), however, should lead to

more (less) intense simulated TCs. Although not un-

dertaken in this project, a logical extension of this re-

search would be to test the surface parameterization

schemes on real and idealized cases while utilizing ex-

change coefficients that are more consistent with ob-

servations.

If future observational field programs are able to ob-

tain flux measurements beneath the TC eyewall at wind

speeds above 30 m s21, then corrections to model ex-

change coefficients will emerge. Comparisons of results

from simulations with the revised SL schemes should be

compared with observationally derived MPI values to

best calibrate the models. With accurate model ex-

change coefficients at high wind speeds over water, im-

provements in TC intensity forecasting may be within

reach. Coupled ocean–wave–atmosphere models, of the

type discussed by Chen et al. (2007) perhaps offer the

best hope for improvement of these important param-

eterization schemes, as the turbulent exchanges of heat,

moisture, and momentum over water in the real atmo-

sphere cannot be realistically parameterized as func-

tions of wind speed alone.

Acknowledgments. This research was funded by NSF

Grant ATM-0334427, awarded to North Carolina State

University. The WRF model was made available

through NCAR. We thank Dr. Mike Brennan (TPC)

and three anonymous reviewers for useful comments

on a previous version of this manuscript.

APPENDIX

Calculating Surface Layer Exchange Coefficients

The exchange coefficients CQ, Cu, and CD are not

output directly from the model, but are computed di-

agnostically using model-calculated fields. Both CQ and

Cu are calculated using the output variables FLQC and

FLHC, respectively. FLQC and FLHC are the ex-

change coefficients for moisture and heat, respectively,

but have the unit of meters per second. The surface

layer schemes calculate moisture and heat fluxes using

the following equations:

QFX 5 FLQC(QSFC�QX) and (A1)

HFX 5 FLHC(THGB� THX), (A2)

where QFX and HFX are moisture and heat flux,

QSFC and QX are mixing ratios at the surface and at

the 10-m level, and THGB and THX are the potential

temperature values at the surface and at the 10-m level.

Rearranging (A1) and (A2), FLQC and FLHC become

the following:

FLQC 5QFX

QSFC�QXand (A3)

FLHC 5HFX

THGB� THX. (A4)

In a bulk formula framework, the fluxes are calculated as

QFX 5 raVaCQ(QSFC�QX), (A5)

HFX 5 racpVaCu(THGB� THX), (A6)

where ra is air density at the 10-m level, cp is the heat

capacity of dry air at constant pressure, Va is the wind

speed at the 10-m level, and CQ and Cu are the ex-

change coefficients for moisture and heat, respectively.

Rearranging (A5) and (A6), the exchange coefficients

are

CQ 5QFX

raVa(QSFC�QX)and (A7)

Cu 5HFX

racpVa(THGB� THX). (A8)

After plugging in (A3) into (A7) and (A4) into (A8),

we get expressions for the exchange coefficients:

CQ 5FLQC

raVaand (A9)

Cu 5FLHC

racpVa. (A10)

As previously stated, FLHC and FLQC are output

from the model. The other variables in the equations

were defined as follows:

d Air density ra at the 10-m level is not standard out-

put from the WRF model, so this quantity was calcu-

lated using a linear interpolation for temperature

(between the 2-m value and the value at the lowest

model level) and for pressure (between the surface

value and the value at the lowest model level).d For this calculation of Va, the model’s 10-m wind

speed (which is standard output) was used.

To calculate the drag coefficient CD, the following

equation was used:


CD 5 u2

*/V2a, (A11)

where u*

is the friction velocity output by WRF and Va

is defined as above.

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