Large Eddy Simulation on Turbulencein the Atmospheric Boundary Layer over the Ocean
under the Pacific Subtropical HighTaro Shinoda, Kazuhisa Tsuboki, Atsushi Sakakibara, and Kenji Nakamura
Hydrospheric Atmospheric Research Center, Nagoya University,
Chikusa-ku, Nagoya, 464-8601, JAPANTEL: +81-52-789-3494, FAX: +81-52-789-3436
E-mail: shinoda@rain.hyarc.nagoya-u.ac.jp

1

Introduction

An atmospheric boundary layer (ABL) over the ocean
under a subtropical high has an important role in thelarge-scale atmospheric circulation. Eﬀects of verticalmixing of heat and moisture in the ABL counteract
those of drying and warming of the large-scale subsidence under the subtropical high. Shallow convective
clouds generated in the ABL enhance the mixing ofheat and moisture, thus they increase surface evaporation over the sea surface. Recently, according toa great progress of the computational ability, highresolution three-dimensional large eddy simulations(LES) are used to investigate the structure of turbulence in the ABL. Stevens et al. (2001) showed thatthe convective circulation was distinctly separated between cloud and subcloud layers over the eastern Atlantic Ocean under a subtropical high. The subcloudlayer located under the cloud layer and was corresponding to the convectively well-mixed layer. There
were streak or plume type circulations in the subcloud layer. The circulation in the cloud layer wascharacterized by buoyant elements in the convective
core and compensating subsidence. Cumulus clouds
formed in the cloud layer had their roots in the subcloud layer, thus the updraft regions were extending
from around the surface into the convective core.
There have been many studies of observation andsimulations over the trade wind regions. However,there have been less ﬁeld observations of the ABL in
the western Paciﬁc Ocean under the subtropical high.
In August 2002, we carried out an intensive observation in order to examine the thermodynamic ﬁelds ofturbulent eddies in the ABL around the Southwest
Islands of Japan (Shinoda et al. 2004). We were able
to separate the subcloud and cloud layers by using
vertical gradient of potential temperature and mixing ratio of water vapor obtained by the radiosonde
observations. By using the Aerosonde observation,
we were able to distinguish two types of eddies. One
was the plume type eddies observed in the lower sub-cloud layer. Since potential temperature and mixing
ratio of water vapor increased simultaneously in theplume type eddies, thus this showed upward transport of a warm and moist air mass around the surface.
The other was the entrainment type eddies observedin the cloud and upper subcloud layers. In the entrainment type eddies, when an anomaly of potential
temperature was positive (negative), an anomaly ofmixing ratio of water vapor was negative (positive)and downward (upward) vertical velocity existed.
However, we have not been able to conﬁrm thestructure of both types of eddy in detail, for example, top height of plume and whether shallow cumulus clouds has their roots in the subcloud layer ornot, because of the lack of data on vertical velocity
by the Aerosonde data. In this study, we examine
a high-resolution three-dimensional LES for the observed turbulent eddies in the ABL around the Southwest Islands under the Paciﬁc subtropical high.

2Model Description

We utilize the Cloud Resolving Storm Simulator(CReSS: Tsuboki and Sakakibara 2001) as a threedimensional LES in order to simulate the structure of
the turbulent eddies in the ABL. It includes an 1.5TKE (Turbulent Kinetic Energy) closure scheme fora subgrid-scale parameterization. A bulk boundary
layer parameterization (Louis 1979) and a Kesslertype warm rain parameterization are used.
The horizontal model domain has 100 × 100 grid
points, and the horizontal grid size is taken to be
100m that is enough to express eﬀects of turbulent
plumes in the ABL (Shinoda 2001). The vertical gridsize is 50 m below 3 km.
The cyclic boundary is used as the lateral boundarycondition. The top boundary is rigid and a sponge
layer is included above the height of 3 km to prevent the reﬂection of internal gravity waves at the topboundary. A lower boundary condition of whole gridsof the model domain is set on a sea surface. An ini-Relative Humidity (%)
4060
80
100

PT
EPT

Qv
RH

800

3

Vertival Velocity at 425 m (m/s)

Case: 02082400Z

06210-1-2900

300
320340Temperature (K)48121620
Mixing Ratio of Vapor (g/kg)

Fig. 1 Profiles of the initial condition for the simulation; that is, sounding at Shimoji Island at 00Z
on August 24, 2002. Potential temperature (solidline in the left panel), equivalent potential temperature (broken line in the left panel), mixing ratioof water vapor (solid line in the right panel), andrelative humidity (broken line in the right panel)are drawn.

2345Time (hour)

789Fig. 2 Time series of maximum and minimum vertical velocity and grid number of convective core:that is, vertical velocity exceeds 0.5ms−1 .

Case: 02082400Z
2.0Height (km)1000110800 sec.
Y = 2.0 km(a) W (m/s) + PT (K)304

1.53031.03020.5301
300
03Results of the LES

Now we show the results of the simulation. Figure 2shows time series of maximum and minimum verticalvelocity at the height of 425 m in the simulation. By
the third hour the ﬂow is relatively stationary. Themaximum vertical (updraft) velocity reaches about
1.5ms−1 at this level. Time series of a ratio of theconvective core deﬁned by grids that the vertical velocity is larger than 0.5ms−1 , to the all grids of themodel domain is also shown in Fig. 2. The ratio is
between 5 and 9% after 3 hours in this simulation.
This level is included in the subcloud layer in theobservation results, therefore, we consider that theseupdrafts are corresponding to the plumes.
Figure 3 shows vertical cross sections of potential
temperature and mixing ratio of water vapor with

Height (km)

2.0K

320
dum0.0tial SST is 302.16 K and the SST varies according toa diurnal variation of shortwave radiation. Forcingsof this simulation are sensible and latent heat ﬂuxes
from the sea surface. These heat ﬂuxes are prescribedby a surface-energy-budget equation.
We simulate the structure of the turbulent eddies
in the ABL observed by the Aerosonde on August24, 2002. Initial condition is taken from the 00 Z
sounding at Shimoji Island on August 24, 2002 shownin Fig.1. There is a strong inversion layer at theheight of 840 hPa (about 1.6 km). A well-mixed layer(subcloud layer) exists between surface and 940 hPa(about 0.7 km), and there is a conditionally unstablelayer (cloud layer) over the subcloud layer.

1000
900
800
700
600
500
400
3002001000Conv. Core Grid (/10000)

Height (hPa)700

20Velocity (m/s)

00Z, Aug. 24, 2002
Shimoji Island

12

345

6

7

8

910(b) W (m/s) + Qv (g/kg)

g/kg

18
17
16
15
14
130dum

1.5
1.0
0.5
0.0
0

12

3

4
5
6Distance (km)78910Fig. 3 Vertical cross sections of potential temperature (a), and mixing ratio of water vapor (b), withvertical wind speed (contour) at 3 hours later fromthe starting of the simulation. Contours for theupdraft (solid line) and downdraft (broken line)
are every 0.2ms−1 .

vertical wind speed at 3 hours later from the starting of the simulation. Some plumes described by theupdraft regions develop in the subcloud layer. The
most plumes are rooted in the lower subcloud layer.
Though only a part of them reaches over a height of
1 km, most of these plumes develop a height of 0.6km. The horizontal scale of the plumes is about 500
m. However, we cannot simulate generation of cumulus clouds around the upper portion of the plumes,
though we have observed shallow convective clouds
during this period.
Figure 4 shows scattered diagrams between verticalvelocity and anomaly of virtual potential temperatureand between anomaly of potential temperature andthat of mixing ratio of water vapor at the height of 125
m and 625 m at 3 hours later from the starting of thesimulation. At the height of 125 m (the lower level ofthe subcloud layer), there is a trend that the anomaly
of virtual potential temperature increases (decreases)

00Z Aug. 24, 2002 (Initial) + 3 hours
1.0

0.0

-0.1

-0.2

PTv Perturbation (K)0.2

012W (m/s)
Perturbation: W vs PTv (625m)

0.1

0.0

-0.1

-0.2
-2

-1

0
W (m/s)

1

2

0.5

0.0

-0.5

304

1.5

303

1.0

302

0.5

2.0

-0.1
0.0
0.1
0.2
PT Perturbation (K)Perturbation: PT vs Qv (625m)

0.5

301
300
12

3

4

5

6

78910(b) W (m/s) + Qv (g/kg) + Qc (g/kg)

g/kg

1918

1.5

171.0160.5

150dum

0.0
0

0.0

-0.5

-1.0
-0.2

-0.1
0.0
0.1
PT Perturbation (K)0.2

Fig. 4 Scattered diagrams between vertical velocity and anomaly of virtual potential temperature and between anomaly of potential temperature and that of mixing ratio of water vapor at theheight of 125 m and 625 m at 3 hours later fromthe starting of the simulation.

in the updraft (downdraft) region. It shows that updrafts are attribute to positive buoyancy by positive
anomaly of virtual potential temperature. There isa weak trend that the anomaly of potential temperature decreases (increases) when the anomaly of mixing ratio of water vapor increases (decreases). However, positive anomaly of mixing ratio of water vapor is enough to oﬀset the weak negative anomaly ofpotential temperature for buoyancy forcing. Therefore, in the updraft region, positive anomaly of virtual potential temperature is corresponding to positive anomaly of mixing ratio of water vapor, not topositive anomaly of potential temperature. This phenomenon should be attributed to the weak forcing bysensible heat ﬂux and abundant supply of water vapor
as latent heat ﬂux from the sea surface. In the lower
subcloud layer, a moist air mass compared with theenvironment transported to the upward. This type of
turbulent eddies can be regarded as a “plume” type.
At the height of 625 m (around the boundary between the subcloud and cloud layers), there is a trendthat the anomaly of virtual potential temperature isnegative (positive) in the updraft (downdraft) region.
Also, there is a trend that the anomaly of potential
temperature decreases (increases) when the anomalyof mixing ratio of water vapor increases (decreases).
In the updraft region, there is a negative anomalyof potential temperature and a positive anomaly ofK

320
dum

0

1.0

10800 sec.
Y = 8.0 km(a) W (m/s) + PT (K)

0.0

-1.0
-0.2-1Qv Perturbation (g/kg)

-2

2.0

Height (km)0.1

Case: 02082400Z_M10

Perturbation: PT vs Qv (125m)

Height (km)Perturbation: W vs PTv (125m)
Qv Perturbation (g/kg)

PTv Perturbation (K)0.2

123456Distance (km)78910Fig. 5 Vertical cross sections of potential temperature (a) and mixing ratio of water vapor (b) withvertical wind speed (thin contour) and mixing ratio of cloud water (bold contour) at 3 hours laterfrom the starting of the moist (relative humidity+10%) simulation. Contours for the updraft are
every 0.2ms−1 and for the cloud water are drawn
at intervals of 0.1, 1.0, 5.0gkg−1 .

mixing ratio of water vapor. This shows the upward
transport of a cool and moist air mass from the subcloud layer. This cool air mass in the updraft region
is attributed to the adiabatic cooling by expansion in
the upper subcloud layer. In the downdraft region,
there is a positive anomaly of potential temperature
and a negative anomaly of mixing ratio of water vapor. This shows the downward intrusion of a warmand dry air mass from the upper region. This type of
turbulent eddies can be regarded as an “entrainment”
type.
These simulated results that two types of eddies
exist in the subcloud layer are corresponding to theobservation results by the Aerosonde. However, wecannot conﬁrm eﬀects of shallow cumulus clouds in
the ABL, because of no development of these clouds
in the simulation.

4Sensitivity tests on humidity

One possibility that shallow cumulus clouds do notdevelop in the simulation is an underestimation ofrelative humidity in the ABL by the sounding observation. Some reports showed that there is a dry
bias in Vaisala radiosonde relative humidity measurements (e.g., Miller et al. 1999). Indeed, mixing ratio observed by the radiosonde is lesser about 1.0 to2.0gkg −1 than that by the Aerosonde during this observation. Therefore, we perform sensitivity tests thatthe relative humidity in all layers changes +5% and+10%. Since shallow cumulus clouds develop in theABL in these moist simulations, we can examine therelationship between the plumes in the subcloud layer
and cumulus clouds in the cloud layer.
Figure 5 shows vertical cross sections of potential
temperature and mixing ratio of water vapor withvertical wind speed and mixing ratio of cloud waterat 3 hours later from the starting of the moist (relative humidity +10%) simulation. Shallow cumulus
clouds depicted by cloud water develop over the subcloud layer. The cloud base height of these clouds is
between 0.7 and 0.8 km, and some cumulus clouds
reach at the height of 1.6 km. The horizontal scale ofcumulus clouds is between 500 m to 1000 m. Ones ofcumulus clouds have their roots in a subcloud layer,
however, the others of them are not rooted in thislayer. In the cumulus clouds, updraft velocity is larger
than 3ms−1 in the convective core, and is larger thanthat in the plumes in the subcloud layer. The potential temperature and mixing ratio of water vapor
in these cumulus clouds exceeds those of the environment by about 1.0K and 2.0gkg −1 , respectively. Itshows that the warm and moist air mass is generated
by condensation heating in the cumulus cloud and istransported to the upper portion of the cloud layer.
The fact that shallow cumulus clouds are generated
in the moist simulation shows that the developmentof cumulus clouds; that is, the vertical transport ofwater vapor from the subcloud layer into the cloudlayer, is sensitive to relative humidity in the cloudand subcloud layers.

5Concluding Remarks

By using the CReSS with 100 m horizontal grid resolution, we examine the structure of the turbulent eddies in the ABL over the ocean around the Southwest
Islands under the Paciﬁc subtropical high. We candistinguish two types of turbulent eddies in the subcloud layer. These results are corresponding to theobservation results utilizing by the Aerosonde; thatis, the plume type turbulent eddies signiﬁcantly exist
in the lower subcloud layer, and the entrainment typeturbulent eddies occupy in the cloud and upper subcloud layers. In the updraft region of plumes, positive
anomaly of mixing ratio of water vapor is enough tooﬀset the weak negative anomaly of potential temperature for buoyancy forcing. Therefore, positive
anomaly of virtual potential temperature that form
updraft is corresponding to positive anomaly of mixing ratio of water vapor, not to positive anomaly ofpotential temperature. This phenomenon should beattributed to the weak forcing by sensible heat ﬂux
and abundant supply of water vapor as latent heatﬂux from the sea surface. In the entrainment typeeddies, the downward intrusion of a warm and dry
air mass from the upper region and the upward transport of a cool and moist air mass from the subcloudlayer are simulated. This cool air mass in the updraft region is attributed to the adiabatic cooling byexpansion in the upper subcloud layer.
The fact that shallow cumulus clouds are generated
in the moist simulation shows that the developmentof cumulus clouds; that is, the vertical transport ofwater vapor from the subcloud layer into the cloudlayer, is sensitive to relative humidity in the cloudand subcloud layers.

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