Impacts of the Lowest Model Level Height on the Performance of PlanetaryBoundary Layer Parameterizations

HYEYUM HAILEY SHIN AND SONG-YOU HONG

Department of Atmospheric Sciences and Global Environment Laboratory, Yonsei University, Seoul, South Korea

JIMY DUDHIA

Mesoscale and Microscale Meteorology Division, NCAR, Boulder, Colorado

(Manuscript received 2 February 2011, in final form 1 July 2011)

ABSTRACT

The lowest model level height z1 is important in atmospheric numerical models, since surface layer similarity

is applied to the height in most of the models. This indicates an implicit assumption that z1 is within the surface

layer. In this study, impacts of z1 on the performance of planetary boundary layer (PBL) parameterizations are

investigated. Three conceptually different schemes in the Weather Research and Forecasting (WRF) model are

tested for one complete diurnal cycle: the nonlocal, first-order Yonsei University (YSU) and Asymmetric

Convective Model version 2 (ACM2) schemes and the local, 1.5-order Mellor–Yamada–Janjic (MYJ) scheme.

Surface variables are sensitive to z1 in daytime when z1 is below 12 m, even though the height is within the

surface layer. Meanwhile during nighttime, the variables are systematically altered as z1 becomes shallower

from 40 m. PBL structures show the sensitivity in the similar manner, but weaker. The order of sensitivity

among the three schemes is YSU, ACM2, and MYJ. The significant sensitivity of the YSU parameterization

comes from the PBL height calculation. This is considerably alleviated by excluding the thermal excess term

in determining the PBL height when z1 is within the surface layer. The factor that specifies the ratio of

nonlocal transport to total mixing is critical to the sensitivity of the ACM2 scheme. The MYJ scheme has no

systematic sensitivity, since it is a local scheme. It is also noted that a numerical instability appears accom-

panying the unrealistic PBL structures when the grid spacing in the surface layer suddenly jumps.

1. Introduction

The surface layer is defined as the region at the bottom

10% of the boundary layer where turbulent fluxes and

stress vary by less than 10% of their magnitude (Stull

1988). According to this definition, the surface layer

height is typically the order of 100 m in daytime convec-

tive boundary layers and the order of 1–10 m in nighttime

stable boundary layers. In most atmospheric numerical

models the lowest model level height (hereafter z1) is

assumed to be within the surface layer height, and surface

layer similarity is applied to z1 whether or not the height is

within a ‘‘real’’ surface layer. Based on this assumption

and surface layer similarity, surface layer schemes in nu-

merical models calculate surface momentum, heat, and

moisture fluxes using data at the surface and z1. When the

models are coupled to a land surface model, the surface

layer schemes calculate surface momentum flux and ex-

change coefficients, and surface heat and moisture fluxes

are calculated by the land surface model. Surface fluxes

from surface layer schemes and surface models serve as

lower boundary conditions in planetary boundary layer

(PBL) parameterizations for vertical transport of surface

forcing (i.e., surface fluxes). In addition, some PBL pa-

rameterizations are designed to be strongly coupled with

surface layer properties. In this context, the externally

determined lowest model level height can influence the

behavior of a PBL scheme, which in turn affects the

performance of prediction skill for atmospheric states.

The importance of the lowest model level height in

atmospheric numerical models has recently been dis-

cussed by a few previous studies (Wei et al. 2001; Zangl

et al. 2008; Aligo et al. 2009). Wei et al. (2001) examined

how modifications of the height of the lowest model level

can alter simulated surface heat fluxes and accompanying

Corresponding author address: Song-You Hong, Dept. of At-

mospheric Sciences, College of Science, Yonsei University, Seoul

120-749, South Korea.

E-mail: shong@yonsei.ac.kr

664 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

DOI: 10.1175/MWR-D-11-00027.1

� 2012 American Meteorological Society

snowmelt during a strong warm-advection snowmelt

event. The surface layer is always stable in this environ-

mental condition. Therefore, the frequently used height

of the lowest model level in global and regional models—

several tens of meters—is beyond the applicable range of

surface layer similarity, and surface sensible and latent

heat fluxes are large enough to be affected by the selec-

tions of z1 under this environmental condition. Wei et al.

concluded that sensible and latent heat fluxes are un-

derestimated when z1 is higher than the real surface layer

depth, which in turn drives an underestimate of the sim-

ulated snowmelt. Zangl et al. (2008) showed that simu-

lations of Alpine foehn are systematically dependent on

the lowest model level height; the dependence on the

height is larger and more systematic than the dependence

on PBL parameterization selection. For quantitative pre-

cipitation forecasts over the Midwest, Aligo et al. (2009)

demonstrated that precipitation forecasts are quantita-

tively improved when z1 is lowered from 54 to 10 m. It

is noted that during daytime convective initiation, the

lower atmosphere is stabilized because of heavy cloud

shading and wet surfaces. These previous studies com-

monly targeted stable surface layers where the com-

monly used z1 of roughly 30–50 m violates the surface

layer assumption; z1 is higher than the real surface layer

height. These prior studies suggested the improvement

of numerical simulations by lowering z1 when the sur-

face layer is stable. To the authors’ knowledge, there is

no literature that examined impacts of z1 on the result-

ing PBL structures when the environment is unstable.

This kind of investigation is important because the lowest

model level height is kept nearly constant during model

integration regardless of environmental regime changes

between unstable and stable conditions.

In this study, impacts of the lowest model level height

on the performance of PBL parameterizations are in-

vestigated for three PBL schemes in the Weather Re-

search and Forecasting (WRF) model, for one complete

diurnal cycle from the Cooperative Atmosphere–Surface

Exchange Study—1999 (CASES-99; Poulos et al. 2002)

field experiment that contains both unstable and stable

surface layer conditions. A brief review of PBL param-

eterizations and possible impacts of z1 on the parame-

terizations is provided in section 2. Experimental setup

and simulation results are given in sections 3 and 4, re-

spectively. Conclusions follow in the final section.

2. Overviews of three PBL parameterizations andcoupling to surface layer

a. PBL parameterizations

PBL parameterizations express effects of subgrid-

scale turbulent motions to prognostic mean variables

(C; u, y, u, q). The most frequently used relation is the

vertical diffusion formula

›C

›t5 2

›

›zw9c9 5

›

›z

�Kc

›C

›z

� ��, (1)

where Kc is the diffusivity for the mean variable C. This

approximation is commonly called K theory (Stull 1988).

Three conceptually different parameterizations—the

Yonsei University (YSU; Hong et al. 2006; Hong 2010),

the Asymmetric Convective Model version 2 (ACM2;

Pleim 2007b), and the Mellor–Yamada–Janjic (MYJ;

Janjic 1990)—are selected for testing possible impacts of

z1 on modeled surface and PBL structures. The YSU

and ACM2 schemes are nonlocal, first-order closure

schemes. For the convective boundary layer (CBL) both

use the K-profile approach, and they consider nonlocal

mixing by large convective eddies. However, they are

distinct from each other mainly in their nonlocal mixing

formulations, as well as in their definitions of PBL height

h and expressions of entrainment fluxes. The YSU PBL

parameterization explicitly expresses nonlocal mixing of

heat and momentum by adding a gradient adjustment

term to the local gradient of each prognostic mean vari-

able (Noh et al. 2003). The ACM2 PBL parameterization

explicitly has a nonlocal upward transport from the surface

and an asymmetrical layer-by-layer downward transport

from the adjacent upper level (Pleim 2007a), for prog-

nostic variables of heat, momentum, and moisture. For the

stable boundary layer (SBL), the YSU scheme uses an

enhanced vertical diffusion of Hong (2010), which is based

on the bulk Richardson number between the surface layer

and the top of the boundary layer. The ACM2 scheme

uses a local mixing method in which the mixing coefficient

is a function of the local Richardson number at a given

model level. As a result of these differences, the YSU and

ACM2 schemes produce divergent PBL structures (Shin

and Hong 2011, hereafter SH11). Note that Hu et al.

(2010) found the two schemes to be quite similar to each

other for a different case: 4-km WRF simulations over

Texas in July–September 2005.

The MYJ parameterization is classified as a local,

1.5-order closure [i.e., turbulent kinetic energy (TKE)

closure] scheme, and it only treats local mixing for both

CBL and SBL (i.e., a local scheme). The diffusion co-

efficient is a function of a prognostic TKE at a given

model level. Only the MYJ scheme is tested in our

study among the three local TKE closure schemes [i.e.,

the MYJ, the quasi-normal scale elimination (QNSE),

and the Bougeault–Lacarrere (BouLac)] in SH11, since

the QNSE and BouLac schemes are also the local, 1.5-

order closure schemes that have the same sort of link-

age as the MYJ scheme to the surface layer (i.e., to z1;

FEBRUARY 2012 S H I N E T A L . 665

cf. section 2b). Moreover, SH11 showed that behaviors of

the three schemes are analogous to each other for the

present simulation case.

b. Surface flux formulations and their linkage toPBL parameterizations

The fundamental role of the surface models and surface

layer parameterizations in atmospheric numerical models

is to calculate momentum, heat, and moisture fluxes from

the surface to the atmosphere. In the current version of

the WRF model, each PBL parameterization uses par-

ticular surface layer parameterizations (Skamarock et al.

2008): the fifth-generation Pennsylvania State University–

National Center for Atmospheric Research (PSU–NCAR)

Mesoscale Model (MM5) surface layer similarity (Zhang

and Anthes 1982) for the YSU scheme, the Pleim–Xiu

(PX) (Pleim 2006) or MM5 surface layer similarity for the

ACM2 scheme, and the Eta surface layer similarity (Janjic

1990) for the MYJ scheme. These schemes follow the

Monin–Obukhov similarity (Monin and Obukhov 1954).

The surface momentum flux t is proportional to the

surface friction velocity u* through the definition of u*:

jtj 5 r[u9w9s21 y9w9s

2]1/2 5 ru2

*, (2a)

u* 5kU1

ln(z1/z0M) 2 cM

. (2b)

In Eq. (2a), r is the air density; and u, y, and w are the

horizontal and vertical velocity components, respectively.

The prime designates the turbulent part of each variable,

and the subscript ‘‘s’’ designates the surface. In Eq. (2b),

U1 is the wind speed at z1, z0M is the surface roughness

length for momentum, and cM is the stability function for

the momentum. In the surface layer schemes, the friction

velocity is computed following similarity theory [Eq. (2b)],

and then the momentum flux is calculated using Eq. (2a).

In this study, the WRF model is coupled with the Noah

land surface model (Chen and Dudhia 2001; Ek et al.

2003; cf. section 3b). Thus, the surface sensible heat flux H

is calculated in the land surface model instead in the

surface layer schemes, but using the exchange coefficient

CH provided by the surface layer schemes:

H 5 rcpu9w9s 5 2rcpCH(u1 2 us), (3a)

CH 5ku*

ln(z1/z0T) 2 cH

, (3b)

where cp is the specific heat of air at constant pressure,

and us and u1 are the potential temperatures at the surface

and z1, respectively. Here z0T is the surface roughness

length for heat, and cH is the stability function for the

heat. Note that each surface layer scheme has some mod-

ifications in calculating u* and CH, while we only show the

basic expressions.

For the moisture flux, the latent heat flux (LH) is de-

termined as

LH 5 rLvq9w9s 5 Lv(Edir 1 Ec 1 Et), (4)

where Lv is the latent heat of vaporization, Edir is the direct

evaporation from the bare soil, Ec is the canopy reeva-

poration, and Et is the transpiration via canopy and roots

(Chen and Dudhia 2001). The first equalities in Eqs. (3a)

and (4) are always valid since they are the definitions of

two fluxes, while the last equalities are based on empirical

and physical hypotheses. Basically, the surface fluxes in

Eqs. (2)–(4) are calculated with the physical properties of

the surface and z1.

In the YSU scheme, there are four parts that are di-

rectly linked to surface layer variables: surface fluxes

(i.e., 2w9c9s) that are transported to the atmosphere;

gradient adjustment terms gc that account for nonlocal

mixing of PBL; the temperature excess term uT due to

surface buoyancy flux and the temperature at z1 that

directly influence the PBL depth calculation; and verti-

cal diffusivities proportional to the velocity scale ws,

which is a function of surface friction velocity u* and

nondimensional stability functions u valid in the surface

layer. Refer to Eqs. (B6), (A3), (A12), and (A1)–(A2) in

Hong et al. (2006), respectively. The ACM2 scheme is

also directly coupled with surface layer variables in these

same four parts, even though the two schemes are dif-

ferent in expressing the nonlocal transport.

In comparison with the YSU and ACM2 parameteri-

zations, the MYJ scheme is more weakly linked with the

surface layer. Only the surface fluxes, the lower boundary

conditions in the scheme, directly affect near-surface

vertical mixing. However, there are still indirect con-

nections. For example, the TKE at the lowest model level

that is directly influenced by the surface fluxes determines

the eddy diffusivity, and the surface friction velocity af-

fects the vertical wind speed gradients near the surface.

3. Experimental setup

a. Synoptic conditions and boundary layer structures

The CASES-99 main site is near Leon, Kansas (37.68N,

96.78W), and the location is relatively flat with lack of

obstacles and covered by grassland (Poulos et al. 2002).

The location is favored by a clear-sky and dry environ-

ment. Since SH11 already described the synoptic envi-

ronment for the diurnal cycle, we briefly summarize the

synoptic conditions. A high pressure system over the

Texas Panhandle at 1200 UTC 23 October moved

666 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

southeastward over the following 24 h, related to the

movement of the 850-hPa ridge to the CASES-99 main

site from the northwest (not shown).

Figure 1 shows vertical profiles of temperature,

wind speed, and moisture from 1100 UTC 23 October

(0600 LST 23 October) to 1100 UTC 24 October 1999,

provided by radiosonde soundings that were made at Leon,

Kansas (see online at http://data.eol.ucar.edu/codiac/

dss/id545.204). The temperature profile (Fig. 1a) at

1900 UTC 23 October shows a uniformly mixed daytime

boundary layer with roughly 900-m depth. Van de Wiel

et al. (2003) investigated that the turbulence in the night of

23–24 October 1999 over the main site was weak and in-

termittent. This intermittent turbulence and the weak

synoptic thermal advection made the high temperature

of the daytime boundary layer remain until 0300 UTC

24 October, except near the surface where strong radiative

cooling was present. However, the strong surface cooling

and intermittent turbulence decoupled the boundary layer

from the surface friction, and the low-level jet appeared

at 0700 UTC 24 October (Fig. 1b). The strong shears due

to the jet drove turbulent mixing; therefore, the stable

layer between 100 and 1000 m appeared at the time.

Since there was no source of moisture under the dry and

weak synoptic forcing, the changes of moisture profiles

were closely linked to the turbulent mixing (Fig. 1c).

b. Model setup

The Advanced Research WRF (ARW) numerical model

version 3.2 is used, which has a fully compressible and

nonhydrostatic dynamic core. The domain configuration

and physics packages are identical to those used in

SH11, which compared five PBL parameterizations in

the WRF model including the YSU, ACM2, and MYJ

PBL schemes for the same simulation period. The WRF

model is run over spatial domains that consist of a parent

domain and two nested domains centered on the loca-

tion of the CASES-99 main site (37.68N, 96.78W) in the

Lambert conformal space (Fig. 2); a 3-km grid-size do-

main (Do3, 49 3 49) is nested inside a 9-km grid-size

domain (Do2, 49 3 49), which in turn is nested within

a 27-km grid-size domain (Do1, 49 3 49) using a one-way

nesting method. Model integrations are conducted for

24 h from 1200 UTC 23 October (0700 LST 23 October)

to 1200 UTC 24 October 1999, and the three domains

are initialized by the National Centers for Environmental

FIG. 1. Observed vertical profiles of (a) potential temperature (K), (b) wind speed (m s21), and (c) vapor mixing ratio (g kg21) from

1100 UTC 23 Oct (0600 LST 23 Oct) to 1100 UTC 24 Oct 1999, obtained from radiosonde soundings that were made at Leon, KS. In

(b), near-surface wind speed profiles are discontinuous because of missing data.

FIG. 2. Model domain for the 27-km horizontal grid-size experi-

ment (Do1) with terrain heights contoured every 200 m. The two

inner boxes represent domains for the 9-km (Do2) and 3-km (Do3)

grid-size experiments, respectively. The crisscross symbol indicates

the CASES-99 site.

FEBRUARY 2012 S H I N E T A L . 667

Prediction (NCEP) Final Analysis (FNL) data on 18 3 18

grids. Boundary conditions for the outmost 27-km do-

main are also forced by the NCEP FNL data every 12 h.

Physics options for radiation and land surface processes

are fixed for all simulations conducted: the Rapid Radia-

tive Transfer Model for GCMs (RRTMG) longwave ra-

diation (Mlawer et al. 1997) and the Goddard shortwave

radiation (Chou and Suarez 1999) schemes, and the Noah

land surface model (Chen and Dudhia 2001; Ek et al.

2003). Steeneveld et al. (2008) used an observation-based

roughness length z0 of 0.03 m that is valid at the CASES-99

main site, and this study adopts the value in all numerical

simulations. The Kain–Fritsch cumulus parameterization

(Kain and Fritsch 1993) and the WRF Single-Moment

6-Class Microphysics scheme (WSM6; Hong et al. 2004;

Hong and Lim 2006) are selected for cloud processes; the

Kain–Fritsch scheme is taken out in all 3-km grid-size ex-

periments. No explicit horizontal diffusion is included, but

sixth-order numerical diffusion is implicitly induced by the

fifth-order horizontal advection scheme instead.

c. Experimental design

The experiments with the YSU, ACM2, and MYJ

schemes are designated as the YSU, ACM2, and MYJ

experiments, respectively. Sensitivities to the lowest

model level height are analyzed for all three PBL schemes

with the aim to compare reactions of these three PBL

diffusion schemes to changes in z1. The control run uses

a vertical grid system of 28 full-s levels (i.e., 27 half-s

levels or 27 layers) with the model top at 50 hPa, which is

the default vertical grid system1 in the WRF model. Here

s is defined as s 5 (p – ptop)/(psfc 2 ptop), where p is

pressure, psfc is pressure at the surface, and ptop is pressure

at the model top. In the WRF model, horizontal wind

components and thermodynamic prognostic variables are

allocated to the half-s levels, while vertical velocity, ver-

tical turbulent fluxes, and eddy diffusivities are assigned

to the full-s levels (cf. Fig. 3). In the control (CTL) sim-

ulation of each PBL scheme, the lowest (first) and second

full-s levels above the ground are s2 5 0.990 and s3 5

0.978, and the corresponding lowest half-s level height z1

is roughly 40 m. Note that the lowest full-s level is the

ground (i.e., s1 5 1.0).

The lowest model level height is controlled by changing

the value of s2. For each PBL parameterization, 9 ex-

periments with 9 different z1 levels including the CTL

experiment are conducted (Table 1): the SL90 (z1 of

roughly 90 m), SL64, CTL (or SL40), SL24, SL16, SL12,

SL08, SL06, and SL04 experiments. To avoid an enor-

mous jump in layer thickness, a full-s level of 0.990 (i.e.,

s2 of the CTL) is added between z1 and a full-s level of

0.978 (i.e., s3 of the CTL) in the SL24, SL16, and SL12

vertical grid systems (cf. Fig. 3). In the SL08, SL06, and

SL04 grid systems, two s levels at 0.990 and 0.996 are

added between z1 and the full-s level of 0.978. It is noted

that results will focus on the SL90, CTL (SL40), SL16,

and SL04 experiments, because of their representative-

ness of the deep surface layer, frequently used z1, and

FIG. 3. A schematic diagram illustrating the lower vertical levels in the CTL, SL90, SL16, and SL04 experiments.

Dotted and solid lines indicate full-s and half-s levels, respectively.

TABLE 1. A summary of numerical experiments. Vertical levels

added below z1 of the control (CTL) experiment (i.e., below the s

level of 0.990) are underlined, and the number of vertical levels that is

identical to the SL04 (CTL) experiment (i.e., 28 levels) are in boldface.

Expt s1 s2 s3 s4 z1 (m)

No. of full-s

levels

SL90 1.0 0.978 0.964 0.946 90 27

SL64 1.0 0.984 0.978 0.964 64 28

SL40 (CTL) 1.0 0.990 0.978 0.964 40 28

SL24 1.0 0.994 0.990 0.978 24 29

SL16 1.0 0.996 0.990 0.978 16 29

SL12 1.0 0.997 0.990 0.978 12 29

SL08 1.0 0.998 0.996 0.990 8 30

SL06 1.0 0.9985 0.996 0.990 6 30

SL04 1.0 0.999 0.996 0.990 4 30

SL16_L28 1.0 0.996 0.978 0.964 16 28

SL04_L28 1.0 0.999 0.978 0.964 4 28

1 In this study, the term default vertical grid system refers to the

vertical grid system that is given in the sample name list file for the

WRF forecast execute program.

668 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

moderately shallow and extremely stable surface layer. In

the SL90, CTL (SL40), SL16, and SL04 experiments, the

heights of z1 levels are 90, 40, 16, and 4 m, respectively.

Information of the lower full-s levels, the lowest model

level height z1, and the number of vertical layers are

summarized in Table 1. Figure 3 illustrates the vertical

grid system of the lower vertical levels in the CTL (SL40),

SL90, SL16, and SL04 experiments.

4. Results

Here, we aim to answer two questions. First, how do

the three schemes react to the changes in z1? Second, how

do the sensitivities change given the stratification of the

boundary layer (i.e., in the convective regime of daylight

hours vs the stable regime during nighttime)? Discussions

are focused on the results of the 3-km grid-interval ex-

periments. As reference observations, surface measure-

ment data are provided by six 10-m towers surrounding the

CASES-99 main site (see online at http://www.eol.ucar.

edu/isf/projects/cases99/isff.shtml), and vertical profiles are

obtained from radiosonde soundings which were made at

Leon, Kansas (37.48N, 96.48W, 436 m mean sea level; see

online at http://data.eol.ucar.edu/codiac/dss/id545.204).

a. Overview of the model performance

Note that the simulated net surface radiation matches

well with the observed one during the selected day (not

shown), even though the modeled individual upward

and downward longwave radiation fluxes deviate from

those observed due to the warm bias in surface tem-

perature. In the land surface model, the net radiation is

in balance with the surface sensible heat flux, latent heat

flux, and soil heat flux (the residual term is less than

5 W m22; Fig. 4a). Meanwhile in the case of the obser-

vation, the sum of the sensible, latent, and soil heat fluxes

is less than the net radiation flux by about 100 W m22

around noon. In consequence, the simulated surface heat

fluxes are larger than those observed owing to the imbal-

ance in the observed energy budget, as well as due to the

overestimated surface temperature. The closure of the

observed surface energy budget is hard to be achieved

because of the instrumentation error, surface heteroge-

neity, and theoretical assumptions in measuring systems

(Brotzge and Crawford 2003). Oncley et al. (2007) men-

tioned that a possible source of the imbalance is the vertical

flux divergence between the canopy top and flux mea-

surement height, mainly due to the horizontal advection.

For these reasons, discussions are focused on the differ-

ences in sensitivity experiments, rather than on an objec-

tive measure of performance against the observations.

The temporal evolution of the surface layer height is

estimated by averaging values of 0.1h (Fig. 4b); h is the

PBL height that is calculated in each PBL scheme for

each z1. The surface layer height is compared with the

various lowest model level heights that are labeled along

the y axis. The surface layer height varies between 4 and

FIG. 4. (a) Surface energy budget of the YSU (black), ACM2 (red), and MYJ (green) SL40 experiments, with corresponding obser-

vations (gray): the sum of the surface sensible heat flux H, latent heat flux LH, and soil heat flux G (solid), and the net radiative flux (Rnet)

(dotted). (b) Estimated surface-layer height (gray solid) derived by averaging values of 0.1h, where h is the PBL height that is calculated

from the YSU (black dotted), ACM2 (red dotted), and MYJ (green dotted) PBL schemes.

FEBRUARY 2012 S H I N E T A L . 669

100 m during one complete diurnal cycle. It is apparent

that none of the z1 values are representative of the di-

urnal variations of the estimated surface layer depth, and

this is because all tested s2 values are constant and do not

vary in time. The assumption that z1 is within the surface

layer is not valid in the stable regime for most of the z1

values, and z1 values of several tens of meters are not

appropriate during the morning and evening transitions.

b. Surface variables

Figure 5 shows the sensitivities of temporal develop-

ment of simulated sensible heat flux H, latent heat flux

LH, and surface friction velocity u* to z1 with the YSU,

ACM2, and MYJ PBL schemes. The daytime time series

show that the simulated H (Figs. 5a–c) is slightly sensitive

to changes in z1. Even though the sensitivity of H is the

most distinguishable at its peak time (inset), the fractional

differences in H among different z1 values remain small.

The maximum value of H varies between 1.35% (ACM2)

and 2.62% (MYJ) from the maximum of the corre-

sponding CTL experiment. For stable surface layer con-

ditions (i.e., in the nighttime), the ACM2 and MYJ

schemes react to the lowest model level height in similar

ways; the magnitude of H gets smaller as z1 decreases

from 40 to 4 m, whereas it gets larger in the YSU ex-

periments. The increase in z1 from 40 to 90 m does not

result in the systematic sensitivity. In the Noah land

surface model, the potential temperature difference in

Eq. (3a) decreases as z1 decreases. Since all z1 values are

expected to be within the real surface layer in the day-

time (cf. Fig. 4b), the wind and temperature profiles at z1

are logarithmic. On the other hand, CH is proportional to

U1 but inversely proportional to [ln(z1/z0M) 2 cM] 3

[ln(z1/z0T) 2 cH] [Eqs. (2b) and (3b)]; CH increases as

z1 decreases. Thus, a possible explanation for the slight

decrease in the magnitude of H due to the reduction in

z1 is that the decrease in the temperature difference in

Eq. (3a) overwhelms the increase in CH. The simulated

latent heat flux (Figs. 5d–f) is sensitive to changes in z1

only during the daytime when the flux is large enough; the

latent heat flux becomes larger as z1 decreases. Since the

latent heat flux is calculated in the land surface model and

it is in balance with the sensible heat flux, the increase of

LH is related to the energy budget balance in the land

surface model consistent with the H reduction.

In the case of the simulated friction velocity (Figs. 5g–i),

the momentum fluxes near the surface slightly increase as

z1 decreases through the daylight hours with all three PBL

schemes. Here u* is directly calculated in surface layer

schemes, and it is proportional to U1, but inversely pro-

portional to [ln(z1/z0M) 2 cM] [Eq. (2b)]. As mentioned

above, the wind profile at z1 is also expected to be loga-

rithmic. Thus, the impact of z1 on the surface friction

velocity is not significant. Under stable surface layer con-

ditions, the ACM2 and MYJ parameterizations show a

common dependency on the lowest level height; by and

large, u* decreases as z1 decreases from 40 down to 4 m.

Unlike in unstable conditions, large z1 values are beyond

the real surface layer in stable conditions; the wind profile

at z1 (i.e., U1) is no longer logarithmic for these large

values, while [ln(z1/z0M) 2 cM] is taken to be logarith-

mic because of the assumption that z1 is within the sur-

face layer. In this case, U1 increases more rapidly than

[ln(z1/z0M) 2 cM] for the same z1 increase. Therefore, u*increases [Eq. (2b)]. The YSU scheme shows an opposite

behavior compared to the other two PBL schemes.

Sensitivities of time series of simulated 2-m tempera-

ture T2 and 10-m wind speed U10 to z1 are presented in

Fig. 6. Note that T2 and U10 are diagnosed in the surface

layer schemes; they are interpolated between z1 and the

surface using similarity theory. During the daytime,

simulated temperatures of the YSU and MYJ schemes

(Figs. 6a,c) slightly increase when z1 is shallow, such as at

4 m (i.e., the SL04 experiments), reflecting the reduction

in H. Note that the daytime changes in the surface heat

fluxes are related to a resistance formulation of the fluxes

(Stensrud 2007). In other words, the depth that responds

to the sensible heat flux decreases as z1 decreases, and

then the layer responses more quickly to the same flux.

This results in the higher 2-m air temperature, and de-

creases the lower temperature differences in Eq. (3a); the

sensible heat flux eventually decreases. Nonetheless, it is

found that the time step hardly changes the surface out-

come of the experiments (not shown). The ACM2 and

MYJ SL04/SL16 experiments produce more rapid surface-

cooling rates during the day-to-night transition time.

Therefore, with the ACM2 and MYJ schemes, the 2-m

temperature becomes cooler during the nighttime as z1

decreases. On the other hand, the YSU scheme shows

an opposite sensitivity to these two schemes in modeling

the nighttime 2-m air temperature, in accordance with the

opposite sensitivity of H. The trend of sensitivities of the

10-m wind speed to the lowest level height resembles that

of the surface friction velocity (cf. Figs. 6d–f and 5g–i). A

noticeable difference between the sensitivities of U10 and

u* is the larger sensitivity of U10 than u* in nighttime for

the YSU scheme.

Both U1 and u1 2 us of the YSU PBL scheme decrease

as z1 gets closer to the surface, similar to the other two

schemes (not shown). Hence, the opposite sensitivity of H

and u* finversely proportional to [ln(z1/z0T,M) 2 cH,M],

Eqs. (2b) and (3)g from the YSU PBL in the stable regime

is attributed to the stability function (cM or cH) of the

MM5 surface layer scheme. The stability function has

a bigger gap between the very stable regime [e.g., the bulk

Richardson number (Rib) in the surface layer is larger

670 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

than 0.2] and the damped mechanical turbulent regime

(0.0 , Rib , 0.2), compared to the gap of the PX or

Eta surface layer scheme. The magnitude of the stability

function is larger in the very stable regime (cf. cM , 0 in

the stable regime). Since the wind profile almost does not

vary in the vertical when z1 is high (e.g., 90 m; cf. Fig. 10g),

Rib in the surface layer is more likely to be above 0.2.

On the other hand, Rib becomes smaller (i.e., enters the

FIG. 5. Time series of (a)–(c) simulated sensible heat flux (W m22), (d)–(f) latent heat flux (W m22), and (g)–(i) surface friction velocity

(m s21) from experiments with the (left) YSU, (middle) ACM2, and (right) MYJ PBL schemes. For each PBL scheme, results from the SL90

(dot–dashed), CTL (SL40) (solid), SL16 (dashed), and SL04 (dotted) experiments are presented. Observations are designated by gray lines

with crisscross symbols. In (a)–(c), each inset provides a closer look at the heat flux from 1600 UTC 23 Oct to 2000 UTC 23 Oct 1999.

FEBRUARY 2012 S H I N E T A L . 671

mechanical turbulent regime) following the reduction in

z1, owing to the increased wind shear. In this case—the

surface layer is classified into the different regimes ac-

cording to z1—both H and u* are larger with the shallow

z1 in the mechanical turbulent case.

Figure 7 summarizes the performance of the three PBL

schemes according to the nine z1 values in simulating

surface parameters and PBL heights. In the daytime,

variables are insensitive to increases in z1 or they do not

show systematic sensitivity when z1 is higher than 12 m.

However, the model results tend to gradually depend on

z1 when z1 decreases below 12 m, even though the surface

layer assumption is not violated. In the nighttime when

most of z1 values in this study are beyond the applicable

range of the surface layer assumption, the simulations of

most variables are systematically sensitive to z1, as z1

decreases from 40 m. The systematic sensitivities of the

ACM2 and MYJ schemes show the same trend, while the

YSU PBL scheme often shows the opposite behavior to

the other two schemes.

c. PBL structures

Dependencies of the PBL height h on z1 imply a deeper

convective boundary layer in the YSU SL04 and SL16

experiments, while the ACM2 and MYJ PBL schemes

are less sensitive to z1 (Figs. 8a–c). In the YSU scheme h

is determined as the lowest level where the bulk Ri-

chardson number (Rib), between the lowest model level

and z above z1, reaches the critical Richardson number

(Ribcr; Hong et al. 2006):

Rib(z) 5gz[uv(z) 2 us]

uvajU(z)j2, (5)

FIG. 6. As in Fig. 5, but for (a)–(c) 2-m temperature (8C) and (d)–(f) 10-m wind speed (m s21). In (a)–(c), each inset provides a closer look

at the 2-m temperature from 1800 UTC 23 Oct to 0000 UTC 24 Oct 1999.

672 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

where g is the acceleration due to gravity, uva is the virtual

potential temperature at z1, and us is the appropriate tem-

perature near the ground. Here uv(z) and U(z) represent

the virtual potential temperature and horizontal wind speed

at z, respectively. The Ribcr is zero for CBL, whereas it is

greater than zero for SBL (Hong 2010). The us is defined as

us 5 uv(z1) 1 uT

�5b

(w9u9v)0

ws

�, (6)

where uT is the temperature excess of thermals, b is a

proportional constant, and ws is the mixed-layer velocity

scale. The uT is excluded in the SBL. Since uva and us get

warmer (cooler) as z1 becomes closer to the surface in CBL

(SBL), h becomes higher (lower) in the YSU experiments

(Fig. 8a). The ACM2 scheme uses a similar method with-

out the thermal excess term in stable conditions, but uva is

defined as the average virtual potential temperature be-

tween z1 and z [cf. Eq. (20) in Pleim (2007a)]. In unstable

conditions, the mixed layer height zmix is first determined

FIG. 7. Sensitivities to z1 of (a) sensible heat flux (W m22), (b) latent heat flux (W m22), (c) surface friction velocity

(m s21), (d) 2-m temperature (8C), (e) 10-m wind speed (m s21), and (f) PBL height (m) that are averaged over

unstable regimes [i.e., 12 h from 1200 UTC 23 Oct (0700 LST 23 Oct) to 0000 UTC 24 Oct (1900 LST 23 Oct)] (circle

marks) and over stable regimes [i.e., 12 h from 0000 UTC 24 Oct (1900 LST 23 Oct) to 1200 UTC 24 Oct (0700 LST

24 Oct)] (triangle marks) for the YSU (black), ACM2 (red), and MYJ (green) experiments. Observed values for the

unstable and stable conditions are designated by gray solid lines and gray dashed lines, respectively. The axes on the

right in (a) and (b) are for stable conditions.

FEBRUARY 2012 S H I N E T A L . 673

where uv(zmix) 5 us. Then, the PBL height h is diagnosed

similar to the YSU PBL, but with Rib defined between zmix

and the heights above zmix (Pleim 2007a):

Rib(z) 5g(z 2 zmix)[uv(z) 2 us]

uvajU(z) 2 U(zmix)j2, (7)

where uva is an average between uv(z) and us. As z1 de-

creases, zmix increases since us gets warmer. Thus, both

temperature gradient and wind shear between zmix and z

decrease for a fixed z above zmix, then Rib and h are not

as sensitive as in the YSU scheme (Fig. 8b). On the other

hand, the MYJ algorithm determines the PBL height as

the model height where the predicted TKE value reaches

a sufficiently small background value (0.101 m2 s22). The

MYJ parameterization is a local closure and is weakly

linked with the surface layer properties. In the CBL TKE

is generally large and the level where TKE becomes the

background value is far from the surface. Thus, the sur-

face layer quantities hardly affect the TKE at that level

(Fig. 8c); h is not sensitive to z1 as much as that of the YSU

PBL. In the SBL of this study the prognostic TKE is gen-

erally small and below the background value (not shown),

and h is usually equal to the height of the lowest full-s

level above the ground (i.e., s2). Therefore, h gradually

increases as z1 increases.

The simulated potential temperature, vapor mixing ratio,

and wind profiles corresponding to sounding measure-

ments at 1900 UTC 23 October (1400 LST 23 October)

are presented in Fig. 9. Under the SL04 configuration, the

YSU scheme produces a deep mixed layer (Figs. 9a,d,g).

Mixing becomes slightly weaker as z1 increases from 16

to 90 m. On the other hand, the ACM2 scheme simulates

a cooler and wetter PBL with the SL04 setting (Figs. 9b,e),

whereas it is warmer and drier above the top of the PBL.

In the ACM2 scheme, the contributions of the nonlocal

transport and local mixing terms are determined by the

variable fconv and (1 2 fconv), respectively:

fconv 5KHgh

KHgh 2 KH

›u

›z

, (8)

where gh is the countergradient term [cf. Eqs. (15)–(19)

in Pleim 2007a]. As z1 decreases, the stronger mixing

occurs during the early stage of the PBL development

(not shown) due to larger local mixing (cf. Fig. 11b), and

the PBL more quickly reaches a neutral state before

1900 UTC (1400 LST). However, the local mixing de-

creases in the neutral PBL, and then fconv increases.

Pleim (2007a) showed that main effects of the nonlocal

component are to stabilize (therefore, to cool) the lower2/3 of the PBL, and to lower the PBL height (cf. Fig. 2 in

Pleim 2007a). The change of the temperature profiles

according to the z1 reduction can be interpreted as the

effects of the increase in fconv [cf. Fig. 9b in this study and

Fig. 2 in Pleim (2007a)]. The MYJ scheme is nearly in-

sensitive to variations in z1 (Figs. 9c,f,i).

Figure 10 presents the simulated profiles at 0700 UTC

24 October (0200 LST 24 October). The strong SBL

mixing of the YSU PBL is alleviated in the SL04 ex-

periment (Fig. 10a). However, the qy profile indicates

the presence of strongly mixed structures in the residual

layer (roughly between 300 and 1300 m) in the SL04

framework (Fig. 10d). This is attributable to the exces-

sive mixing throughout the whole PBL during the

FIG. 8. As in Fig. 5, but for the PBL heights.

674 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

daytime, as well as the nighttime local mixing (cf.

Fig. 11d). The momentum mixing in the SBL decreases

following the z1 reduction (Fig. 10g), but it is not enough

to simulate the low-level jet (LLJ). Note that all three

schemes are not able to simulate the LLJ with proper

intensity on this night. In the case of the ACM2 scheme

(Figs. 10b,e,h), the lower atmosphere below 1000 m is still

slightly cooler and wetter with the smaller z1, because of

FIG. 9. Vertical profiles of the (a)–(c) simulated potential temperature (K), (d)–(f) vapor mixing ratio (g kg21), and (g)–(i) wind speed

(m s21) at 1900 UTC 23 Oct (1400 LST 23 Oct) 1999 from experiments with the (left) YSU, (middle) ACM2, and (right) MYJ PBL

schemes and corresponding radiosonde soundings (gray lines). For each variable from each PBL scheme, results from the SL90 (dot–

dashed), CTL (SL40) (solid), SL16 (dashed), and SL04 (dotted) experiments are presented.

FEBRUARY 2012 S H I N E T A L . 675

the daytime profiles. The ACM2 scheme produces a

strongly mixed moisture profile in the nighttime (Fig. 10e).

The mixing becomes weaker with the SL04 and SL16

vertical-grid configurations, but they are not enough to

simulate a local minimum at 1000 m as small as in the

other two schemes. The MYJ scheme shows almost no

sensitivity to z1 above the SBL (Figs. 10c,f,i), whereas z1

affects the performance of the three PBL schemes below

the top of the SBL. This is because temperature and wind

profiles significantly change near the surface in the night

FIG. 10. (a)–(i) As in Fig. 9, but at 0700 UTC 24 Oct (0200 LST 24 Oct) 1999. In (g)–(i), wind direction (8) is added. Note that near-surface

wind speed profiles are discontinuous because of missing data [e.g., (g)–(i)].

676 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

time, and the proportion of the SBL that z1 accounts for

varies considerably following z1: from several percent of

the SL04 to almost 50% of the SL90.

The KM (vertical diffusivity for momentum) averaged

over unstable and stable regimes is displayed in Fig. 11. It

is noted that the diffusivity Kc(1 2 fconv) is multiplied by

the local gradient of the prognostic mean variable C to

express local mixing in the ACM2 scheme [cf. Eqs. (10)

and (11) in Pleim 2007a]. Thus, the diffusivity Kc(1 2 fconv)

is depicted in the figure. In unstable regimes, as z1 de-

creases from 90 to 4 m, the maximal magnitude of KM

and mixing depth of the YSU scheme gradually increase

(Fig. 11a). This supports the behavior of the simulated day-

time profiles (Figs. 10a,d,g). The ACM2 scheme (Fig. 11b)

shows a similar sensitivity to the YSU scheme from z1

of 16 to 4 m, but it is not sensitive to the changes in z1

from 90 to 16 m. The KM of the MYJ scheme does not

reveal systematic sensitivity (Fig. 11c). The differences in

z1 sensitivity among the three PBL schemes can be ex-

plained by examining how the diffusivities are formu-

lated in the schemes. In the YSU scheme, the diffusivity

is specified based on the prescribed K-profile functions

[refer to Eq. (A1) in Hong et al. 2006]:

KM 5 kwsz 12z

h

� �2, (9)

where k is the von Karman constant, ws is the mixed-layer

velocity scale, and h is the PBL height. According to this

formula, the diffusivity profiles are limited below the PBL

height, thus the PBL height is very critical in describing the

K profiles. The PBL height gets higher as z1 becomes

smaller in the YSU scheme (cf. Fig. 8a), and it is consistent

with the enhanced diffusivity within the PBL (Fig. 11a).

FIG. 11. Eddy viscosity KM (m2 s21) averaged over 12 h (a)–(c) from 1200 UTC 23 Oct to 0000 UTC 24 Oct (i.e., convective regime), and

(d)–(f) from 0000 UTC 24 Oct to 1200 UTC 24 Oct (i.e., stable regime) from experiments with the (left) YSU, (middle) ACM2, and (right)

MYJ PBL schemes. For each PBL scheme, results from the SL90 (dot–dashed), CTL (SL40) (solid), SL16 (dashed), and SL04 (dotted)

experiments are presented.

FEBRUARY 2012 S H I N E T A L . 677

In the ACM2 scheme, the larger of the K-profile value

[Eq. (1) in Pleim 2007b] and a local K value [K is pro-

portional to local wind shear and local Richardson number,

Eq. (4) in Pleim 2007b] is applied in the CBL. The K-profile

value is generally larger than the local K value in CBL,

except near the top of the PBL. Thus, the ACM2 SL04

experiment shows larger diffusivity in the middle of the

PBL than other ACM2 experiments as in the YSU SL04

experiment (cf. Figs. 11a,b). In the MYJ PBL scheme, the

diffusivities are proportional to turbulent kinetic energy

[i.e., e; refer to Eq. (3.4) in Janjic 1990]:

Kc 5 lffiffiffiep

Sc, (10)

where l is the mixing length, e is the turbulent kinetic en-

ergy, and Sc is the proportionality coefficient. The lowest

model level height has a direct influence only on near-

surface heights in the MYJ scheme, while the local TKE

and mixing length (therefore, the diffusivity) are large in

middle of the PBL, which results in a less systematic sen-

sitivity (Fig. 11c). Generally, KH (vertical diffusivity for heat

and moisture) shows similar behaviors with KM according

to z1 changes (not shown), since KM and KH are linked

to each other. In the YSU PBL algorithm, KM is cal-

culated first, and KH is determined through multiplying

KM by the Prandtl number. In the ACM2 method, KH is

equal to KM.

In stable regimes, the manners in which diffusivities

change in accordance with z1 differ among the PBL

schemes (Figs. 11d,e,f). In the YSU scheme, the pre-

scribed K-profile method [Eq. (9)] is used in stable re-

gimes, unlike the local K method of the ACM2 and

MYJ schemes. Therefore, the diffusivities gradually get

smaller through lowering z1 within the SBL (Fig. 11d),

following the decrease in SBL height (cf. Fig. 8a). This

explains the weaker mixing in the lower z1 experiments

(Figs. 10a,d,g). Meanwhile, the diffusivities above the SBL

increase following the z1 reduction in the SL04 experi-

ment. The height of the larger KM of the SL04 experi-

ment (i.e., between 500 and 1000 m above the ground)

matches well with the height where the wind direction

changes more with time compared to other vertical grid-

spacing experiments (not shown). The vertical gradient of

the wind speed is also larger with height (e.g., Fig. 10g).

Changes in inertial oscillations following the z1 reduction

seem to play a role in increasing the vertical wind shear in

the nighttime. The diffusivities are proportional to the

local wind shear above the SBL [cf. Eq. (A15) in Hong

et al. 2006], and this explains the increases of Kc above the

SBL. The ACM2 experiments show that diffusivities in-

crease when z1 is between 90 and 40 m (Fig. 11e; i.e., from

SL90 to SL64, and then to SL40); however, they decrease

when the height is lowered from 40 down to 4 m. It is

noted that the diffusivities are set as the background

value when the local Richardson number exceeds 0.25 in

the ACM2 PBL scheme: K0 5 0.001Dz (m2 s21). A very

stable near-surface profile is produced when z1 is low, and

the diffusivities are set to K0 near the surface with a large

local Richardson number. The diffusivities of the MYJ

scheme tend to decrease as z1 decreases down to 24 m,

and they are almost invariable when z1 is below 24 m

(Fig. 11f).

Synthesizing the above, the two nonlocal, K-profile PBL

parameterizations—the YSU and ACM2 schemes—are

more sensitive to the lowest model level height than

the local PBL scheme. However, the sensitivities of the

two schemes are different (sometimes, opposite) to each

other, according to the dissimilarities in the definition of

the PBL height, the determination of the diffusivity in

the entrainment zone, and the nonlocal mixing for-

mula. The local MYJ scheme is nearly insensitive to the

height of the lowest model level, except for the stable

regime.

Since we use a one-way nesting method between the

27-, 9-, and 3-km grid spacing domains (cf. section 3b),

we checked whether the z1 sensitivity depends on the

horizontal resolution (not shown). The impacts of z1 of

the 3-km grid-size experiments are kept at the 9-km grid

size. WRF simulations with the 27-km grid spacing also

show the similar sensitivity to z1 to the 3-km grid spacing

simulations, except for surface wind variables during the

morning transition; the magnitude of the surface friction

velocity and 10-m wind speed suddenly decreases during

the transition unlike the 9- and 3-km experiments.

Another issue is the impact of evening transition sim-

ulations on the z1 sensitivity for stable conditions, since the

WRF simulations in our study are begun in early morning.

It is well known that simulating the evening transition

from a CBL to an SBL is a common deficiency of many

atmospheric numerical models (Edwards et al. 2006). A

second set of experiments, which are initiated at 0000 UTC

24 (1900 LST 23) October 1999, showed that the z1

sensitivities of the three PBL schemes are generally kept

whether the evening transition is simulated by the WRF

model or provided from the NCEP FNL data (not

shown). However, for vertical profiles, the strongly mixed

moisture profiles resulting from the excessive daytime

mixing in the two nonlocal schemes (Figs. 10d,e) are re-

moved when the simulations are started in early evening

(not shown); the PBL structures are insensitive to the

lowest model level height above the SBL.

d. Importance of vertical grid spacing insurface layer

In the experiments with z1 below 40 m, the vertical grid

spacing in surface layer becomes finer as z1 decreases (cf.

678 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

Fig. 3 and Table 1). Increasing the number of the vertical

levels is done to avoid a sudden jump in layer thickness

between the first and second layers, but this also results in

a refined vertical grid resolution in the surface layer. To

discuss the importance of vertical grid spacing in surface

layer, SL16_L28 and SL04_L28 experiments are conducted.

In these cases, we lower z1 without adding vertical layers

(i.e., with 28 full-s levels; Table 1); the z2 values of the

two experiments are 100 and 90 m, respectively.

In section 4b, it is mentioned that the surface and 2-m

air temperatures increase through lowering z1, consistent

with the resistance formulation of the fluxes. On the other

hand, the second vertical layer is excessively deeper than

z1 in the SL04_L28 experiments. Then, the second layer

responds more slowly to the heated first layer in

comparison with the SL04 experiments; the heat from the

surface is accumulated in the lower layer. On account of

this, the maximum surface and 2-m air are warmer by

about 2 (YSU) to 4 K (ACM2) than the SL04 experi-

ments (not shown). Owing to this increased near-surface

temperature, the YSU and ACM2 SL04_L28 experiments

produce an overly deep mixed layer, and the moisture

profiles are significantly deteriorated (Figs. 12a,b). These

degraded structures remain in the residual layer in the

nighttime (Figs. 12d,e). Opposite to the two schemes, the

MYJ SL04_L28 experiment shows a shallower mixing in

the CBL (Fig. 12c). This is attributed to the accumulation

of the TKE at the first layer and the decrease in TKE

above (not shown), leading to the decrease in the diffu-

sivity in the PBL [cf. Eq. (10)].

FIG. 12. (a) Vertical profiles of the simulated vapor mixing ratio (g kg21) at (a)–(c) 1900 UTC 23 Oct and (d)–(f) 0700 UTC 24 Oct 1999,

from experiments with the (left) YSU, (middle) ACM2, and (right) MYJ PBL schemes. Results from the SL90 (dot–dashed black), CTL

(SL40) (solid black), SL16_L28 (dashed red), and SL04_L28 (dotted red) experiments are presented, with corresponding radiosonde

soundings (gray lines).

FEBRUARY 2012 S H I N E T A L . 679

This ‘‘vertical grid spacing impact’’ (or ‘‘vertical layer

thickness problem’’) is a discretization issue (in the real

world, there is no ‘‘vertical layer thickness,’’ nor layer-by-

layer heat flux). There should be heat flux from the

warmer region to the adjacent cooler region in the real

atmosphere. However, modeled heat flux from the first

layer to the second layer is weaker in the SL04_L28 ex-

periments (not shown) despite the larger temperature

difference between the two layers in the SL04_L28 runs

(the first layer is warmer than the SL04 run, while the

second layer is cooler). This is due to the effect of the

thickness of the second layer that overwhelms the effect

of the temperature difference on the temperature gradi-

ent used for the flux, allowing the buildup of more heat in

the lowest layer.

These results indicate that a shallow vertical layer

thickness near the surface requires more model layers

within the surface layer to better resolve the surface layer.

e. A modification in the YSU PBL parameterization

As shown in section 4c, the sensitivity of the simulated

PBL structures to the lowest model level height mainly

comes from the dependency of the PBL height to z1 in the

YSU PBL parameterization. The major reason of the de-

pendency is the increase in the appropriate near-surface

temperature us of Eq. (6), which is critical in determining

the PBL height [cf. Eq. (5)]. Troen and Mahrt (1986)

mentioned that the most energetic transporting scales of

turbulent motions in the CBL are thermals in the lowest

part of the boundary layer. Therefore, us is considered as

a measure of temperature of the thermals through adding

the thermal excess term uT to the temperature of the

lowest model level uv(z1) [cf. Eq. (6)]. However, uv(z1)

itself increases toward the temperature of the thermals

as z1 approaches the surface. Thus, it is worthwhile to

remove the thermal excess term when z1 is within the

surface layer (i.e., the constant flux layer), and to observe

the impacts of the removal of uT.

We modify the algorithm of the PBL height determi-

nation such that the thermal excess term is included only

if the lowest model level height is above the surface layer

(i.e., only if z1 . 0.1h), with a surface layer height that is

estimated as 0.1h. Here h is calculated using Eq. (5)

without uT. Then, we observe how the modified PBL

height calculation impacts the sensitivity of the YSU PBL

scheme to z1. The experiments without the thermal excess

term are named the SL90_noT, SL40_noT, SL16_noT,

and SL04_noT experiments.

The increase in h is much less when the thermal excess

term is excluded (cf. Figs. 8a and 13a). Note that in the

CBL, the PBL height is O(1 km), and then the surface

layer is estimated as O(100 m). Thus, most z1 values

considered in this study are below 0.1h, and h is reduced

in the most noT experiments. For surface variables, it is

apparent that the YSU PBL scheme responds to z1 in

similar ways with or without the thermal excess term (not

shown). The reason for the similar dependency regardless

of uT is that the differences in h do not directly affect the

surface variables. As discussed in section 4b, the sensi-

tivities of surface fluxes to z1 in daytime mainly come

from the temperature and wind differences between the

surface and z1. It is also mentioned that the sensitivities of

T2 and U10 are dependent on the surface fluxes.

Figures 13b,c present the simulated moisture profiles

of the CBL and SBL, respectively. With the modification

in h, the excessive mixing in the daytime is significantly

alleviated; the decrease in h due to the removal of uT

results in a shallower and smaller vertical diffusivity (not

shown). Because of the reduced mixing in the CBL, the

strongly mixed structure in the residual layer in the SBL

(cf. Figs. 10d and 13c) are eliminated.

5. Conclusions

This paper documented the impacts of the lowest

model level height on the performance of PBL param-

eterizations in simulating surface variables and PBL

structures. Three different PBL schemes were tested

using the WRF model: the nonlocal, first-order YSU and

ACM2 schemes, and the local, 1.5-order MYJ scheme.

In most atmospheric numerical models, the lowest model

level height is assumed to be within the surface layer, and

the assumption is valid with most of the z1 values con-

sidered in this study in daytime. Nevertheless, it was found

that all simulated surface parameters that were taken into

account undergo gradual and slight changes by imposing

a lowest model level height below 12 m in unstable con-

ditions. They are hardly sensitive to z1 or not systemati-

cally dependent on z1 when using a height above 12 m. In

stable conditions, the results showed an asymptotic be-

havior according to changes in z1. In other words, the

results are systematically altered as z1 decreases below

40 m, while they are nearly insensitive to z1 with higher z1.

In simulating vertical profiles, the PBL schemes show

the sensitivity in a similar manner to the surface prop-

erties, but weaker. The YSU scheme is the most sensi-

tive to z1, the ACM2 is the second, and the MYJ scheme

is the least sensitive. These differences in the sensitivity

among the PBL parameterizations result from the differ-

ent formulations of the parameterizations themselves.

The YSU parameterization simulates a deeper convective

boundary layer as z1 decreases, and it is attributed to the

algorithm for calculating the PBL height. This sensitivity

is considerably reduced by excluding the thermal excess

term in determining the PBL height when z1 is within the

surface layer. In the case of the ACM2 PBL, the parameter

680 M O N T H L Y W E A T H E R R E V I E W VOLUME 140

that determines the ratio of the nonlocal transport to the

total vertical mixing is responsible for the sensitivity of the

ACM2 scheme. The MYJ PBL is a local closure scheme,

and it is nearly insensitive to z1. In stable regimes, the

vertical profiles significantly change near the surface and

the proportion of SBL that z1 accounts for varies consid-

erably following z1. Hence, z1 plays an important role in

specifying lower boundary layer profiles.

These impacts of the lowest model level height are

mostly kept at coarser horizontal grid spacing of 9 and

27 km. It was also demonstrated that the evening-transition

simulations hardly affect the dependency of the PBL

schemes to z1 in general, even though the modeled

values themselves are altered. One noticeable change is

the removal of the excessively mixed moisture profiles

above the stable boundary layer, when the model runs

were started in early evening. It is also noted that a nu-

merical instability appears accompanying the unrealistic

PBL structures when there is a significant jump in the

vertical-layer thickness in the surface layer.

Two directions for future study can be suggested:

extending discussions of this issue to different envi-

ronmental conditions besides clear-sky conditions, and

suggesting methods for adequately using the lowest

model level height while not violating the assumption

for the upper limit of z1 (i.e., z1 within the surface layer).

Regarding the first direction, studies on interactions

between z1 impacts and precipitation are relevant be-

cause of increasing interest in high-impact weather and

hydro-climate simulations. For the second direction, an

ideal new method would be to change the lowest model

level height to a new realistic surface layer depth through

every time step. However, this is equivalent to changing

the vertical coordinate, which could induce vertically

unbalanced meteorological fields accompanied by nu-

merical issues related to conservation and stability. Al-

ternatively, it is challenging to use a time-varying surface

layer height inside the surface layer and boundary layer

physics schemes. Related to the importance of vertical

grid spacing in the surface layer, a multilayer surface layer

scheme is also promising.

Acknowledgments. We would like to express our grati-

tude to the four anonymous reviewers, and all of the scien-

tists who were involved in the CASES-99 field experiments.

This research was supported by the Leading Foreign

Research Institute Recruitment Program through the

National Research Foundation of Korea (NRF) funded by

the Ministry of Education, Science and Technology

(MEST) (2010-00715), the Basic Science Research Pro-

gram through the NRF funded by MEST (2011-0000388),

and the Korea Meteorological Administration Research

and Development Program under Grant RACS 2010-

2014. This work was also supported by the second phase of

the Brain Korea 21 Program in 2011.

REFERENCES

Aligo, E. A., W. A. Gallus Jr., and M. Segal, 2009: On the impact of

WRF model vertical grid resolution on Midwest summer

rainfall forecasts. Wea. Forecasting, 24, 575–594.

FIG. 13. (a) Time series of simulated PBL height (m), and vertical profiles of the simulated vapor mixing ratio (g kg21) at (b) 1900 UTC

23 Oct and (c) 0700 UTC 24 Oct 1999. Results from the YSU SL90_noT (dot dashed), YSU SL40_noT (solid), YSU SL16_noT (dashed),

and YSU SL04_noT (dotted) experiments are presented, in parallel with the YSU SL04 experiment (dotted red). Observations are

designated by gray lines.

FEBRUARY 2012 S H I N E T A L . 681

Brotzge, J. A., and K. C. Crawford, 2003: Examination of surface

energy budget: A comparison of eddy correlation and Bowen

ratio measurement systems. J. Hydrometeor., 4, 160–178.

Chen, F., and J. Dudhia, 2001: Coupling an advanced land-surface/

hydrology model with the Penn State/NCAR MM5 modeling

system. Part I: Model description and implementation. Mon.

Wea. Rev., 129, 569–585.

Chou, M.-D., and M. J. Suarez, 1999: A solar radiation parameter-

ization for atmospheric studies. Tech. Rep. Series on Global

Modeling and Data Assimilation, NASA/TM-1999-104606,

Vol. 15, NASA Goddard Space Flight Center, 38 pp.

Edwards, J. M., R. J. Beare, and A. J. Lapworth, 2006: Simulation

of the observed evening transition and nocturnal boundary

layers: Single-column modeling. Quart. J. Roy. Meteor. Soc.,

132, 61–80.

Ek, M. B., K. E. Mitchell, Y. Lin, E. Rogers, P. Grunmann,

V. Koren, G. Gayno, and J. D. Tarpley, 2003: Implementation

of Noah land surface model advances in the National Centers

for Environmental Prediction operational mesoscale Eta

model. J. Geophys. Res., 108, 8851, doi:10.1029/2002JD003296.

Hong, S.-Y., 2010: A new stable boundary-layer mixing scheme and

its impact on the simulated East Asia summer monsoon. Quart.

J. Roy. Meteor. Soc., 136, 1481–1496.

——, and J.-O. J. Lim, 2006: The WRF single-moment 6-class mi-

crophysics scheme (WSM6). J. Korean Meteor. Soc., 42, 129–151.

——, J. Dudhia, and S.-H. Chen, 2004: A revised approach to ice

microphysical processes for the bulk parameterization of

clouds and precipitation. Mon. Wea. Rev., 132, 103–120.

——, Y. Noh, and J. Dudhia, 2006: A new vertical diffusion package

with an explicit treatment of entrainment processes. Mon. Wea.

Rev., 134, 2318–2341.

Hu, X.-M., J. W. Nielsen-Gammon, and F. Zhang, 2010: Evaluation

of three planetary boundary layer schemes in the WRF model.

J. Appl. Meteor. Climatol., 49, 1831–1844.

Janjic, Z. A., 1990: The step-mountain coordinate: Physics pack-

age. Mon. Wea. Rev., 118, 1429–1443.

Kain, J. S., and J. M. Fritsch, 1993: Convective parameterization for

mesoscale models: The Kain-Fritsch scheme. The Representation

of Cumulus Convection in Numerical Models, K. A. Emanuel

and D. J. Raymond, Eds., Amer. Meteor. Soc., 165–170.

Mlawer, E. J., S. J. Taubman, P. D. Brown, M. J. Iacono, and S. A.

Clough, 1997: Radiative transfer for inhomogeneous atmo-

sphere: RRTM, a validated correlated-k model for the long-

wave. J. Geophys. Res., 102, 16 663–16 682.

Monin, A. S., and A. M. Obukhov, 1954: Basic turbulence mixing laws

in the atmospheric surface layer. Tr. Inst. Teor. Geofiz. Akad.

Nauk. SSSR, 24, 163–187. (English translation available in V. N.

Bespalyi, Ed., 2001: Turbulence and Atmospheric Dynamics.

J. L. Lumley, 164–194.)

Noh, Y., W.-G. Cheon, S.-Y. Hong, and S. Raasch, 2003: Im-

provement of the K-profile model for the planetary boundary

layer based on large eddy simulation data. Bound.-Layer

Meteor., 107, 401–427.

Oncley, S. P., and Coauthors, 2007: The energy balance experiment

EBEX-2000. Part I: overview and energy balance. Bound.-

Layer Meteor., 123, 1–28.

Pleim, J. E., 2006: A simple, efficient solution of flux-profile re-

lationships in the atmospheric surface layer. J. Appl. Meteor.

Climatol., 45, 341–347.

——, 2007a: A combined local and nonlocal closure model for the

atmospheric boundary layer. Part I: Model description and

testing. J. Appl. Meteor. Climatol., 46, 1383–1395.

——, 2007b: A combined local and nonlocal closure model for the

atmospheric boundary layer. Part II: Application and evalu-

ation in a mesoscale meteorological model. J. Appl. Meteor.

Climatol., 46, 1396–1409.

Poulos, G. S., and Coauthors, 2002: CASES-99: A comprehensive

investigation of the stable nocturnal boundary layer. Bull.

Amer. Meteor. Soc., 83, 555–581.

Shin, H. H., and S.-Y. Hong, 2011: Intercomparison of planetary

boundary-layer parameterizations in the WRF model for

a single day from CASES-99. Bound.-Layer Meteor., 139,261–281.

Skamarock, W. C., and Coauthors, 2008: A description of the ad-

vanced research WRF version 3. NCAR Tech. Note NCAR/

TN-4751STR, 113 pp.

Steeneveld, G. J., T. Mauritsen, E. I. F. de Bruijn, J. V.-G. de Arellano,

G. Svensson, and A. A. M. Holtslag, 2008: Evaluation of

limited-area models for the representation of the diurnal

cycle and contrasting nights in CASES-99. J. Appl. Meteor.

Climatol., 47, 869–887.

Stensrud, D. J., 2007: Parameterization Schemes: Keys to Under-

standing Numerical Weather Prediction Models. Cambridge

University Press, 459 pp.

Stull, R. B., 1988: An Introduction to Boundary Layer Meteorology.

Kluwer Academic Publishers, 666 pp.

Troen, I., and L. Mahrt, 1986: A simple model of the atmospheric

boundary layer; sensitivity to surface evaporation. Bound.-

Layer Meteor., 37, 129–148.

van de Wiel, B. J. H., A. F. Moene, O. K. Hartogensis, H. A. R. de

Bruin, and A. A. M. Holtslag, 2003: Intermittent turbulence

in the stable boundary layer over land. Part III: A classifi-

cation for observations during CASES-99. J. Atmos. Sci., 60,

2509–2522.

Wei, H., M. Segal, W. J. Gutowski Jr., Z. Pan, R. W. Arritt, and

W. A. Gallus Jr., 2001: Sensitivity of simulated regional

surface thermal fluxes during warm advection snowmelt to

selection of the lowest model layer height. J. Hydrometeor.,

2, 395–405.

Zangl, G., A. Gohm, and F. Obleitner, 2008: The impact of the

PBL scheme and the vertical distribution of model layers

on simulations of Alpine foehn. Meteor. Atmos. Phys., 99,105–128.

Zhang, D., and R. A. Anthes, 1982: A high-resolution model of the

planetary boundary layer—Sensitivity tests and comparisons

with SESAME-79 data. J. Appl. Meteor., 21, 1594–1609.

682 M O N T H L Y W E A T H E R R E V I E W VOLUME 140