The Operational JMA Nonhydrostatic Mesoscale Model · The model is based on the MRI/NPD unified...

The Operational JMA Nonhydrostatic Mesoscale Model

KAZUO SAITO

Meteorological Research Institute, Tsukuba, Japan

TSUKASA FUJITA, YOSHINORI YAMADA, JUN-ICHI ISHIDA, YUKIHIRO KUMAGAI, KOHEI ARANAMI,SHIRO OHMORI, RYOJI NAGASAWA, AND SAORI KUMAGAI

Japan Meteorological Agency, Tokyo, Japan

CHIASHI MUROI, TERUYUKI KATO, AND HISAKI EITO

Meteorological Research Institute, Tsukuba, Japan

YOSUKE YAMAZAKI

Advanced Earth Science and Technology Organization, Tokyo, Japan

(Manuscript received 9 February 2005, in final form 23 June 2005)

ABSTRACT

An operational nonhydrostatic mesoscale model has been developed by the Numerical Prediction Divi-sion (NPD) of the Japan Meteorological Agency (JMA) in partnership with the Meteorological ResearchInstitute (MRI). The model is based on the MRI/NPD unified nonhydrostatic model (MRI/NPD-NHM),while several modifications have been made for operational numerical weather prediction with a horizontalresolution of 10 km. A fourth-order advection scheme considering staggered grid configuration is imple-mented. The buoyancy term is directly evaluated from density perturbation. A time-splitting scheme foradvection has been developed, where the low-order (second order) part of advection is modified in thelatter half of the leapfrog time integration. Physical processes have also been revised, especially in theconvective parameterization and PBL schemes. A turbulent kinetic energy (TKE) diagnostic scheme hasbeen developed to overcome problems that arise to predict TKE. The model performance for mesoscaleNWP has been verified by comparison with a former operational hydrostatic mesoscale model of JMA. Itis found that the new nonhydrostatic mesoscale model outperforms the hydrostatic model in the predictionof synoptic fields and quantitative precipitation forecasts.

1. Introduction

Rapid progress of the computer facilities in recentyears enables us to use higher-resolution models in nu-merical weather prediction (NWP). The horizontalresolution of operational regional/mesoscale models inworld main forecast centers is becoming higher andhigher and is about 10 km, the limit of validity of thehydrostatic approximation. The Deutscher Wetter-dienst (DWD) developed a regional nonhydrostatic

model (the Lokall-Model; Doms and Schaettler 1997)and started its operational run with a horizontal reso-lution of 7 km in 1999. The Met Office introduced non-hydrostatic new dynamics (Davies et al. 2005) in theUnified Model in 2002. The Meteorological Service ofCanada, the National Centers for Environmental Pre-diction of the United States, and other national forecastcenters have also been developing or testing their non-hydrostatic NWP models for operation.

In Japan, the Japan Meteorological Agency (JMA)started operational run of a 10-km-resolution meso-scale model in March 2001, and 18-h time integrationhas been carried out 4 times a day. This model, MSM,was introduced to support information for disaster pre-vention and is also used for the very short range fore-

Corresponding author address: Dr. Kazuo Saito, Second Labo-ratory, Forecast Research Department, Meteorological ResearchInstitute, 1-1 Nagamine, Tsukuba, Ibaraki 305-0052, Japan.E-mail: [email protected]

1266 M O N T H L Y W E A T H E R R E V I E W VOLUME 134

© 2006 American Meteorological Society

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cast of precipitation and for short-term aviation fore-casts. For its initial condition, a four-dimensional varia-tional data assimilation analysis (Meso 4DVAR;Ishikawa and Koizumi 2002) was implemented inMarch 2002. Implementation of the Meso 4DVAR sig-nificantly improved performance of MSM in precipita-tion forecasts; however, to respond the request of thedynamical prediction of heavy rainfall, we need furtherimprovement of model performance. Since MSM is ahydrostatic model, there is a limit in horizontal resolu-tion, which is essentially important to simulate the dy-namical field of heavy rainfall relating to deep convec-tion. It is evident that a high-resolution nonhydrostaticmodel with cloud microphysics must be employed toachieve the dynamical prediction of heavy rainfall.

This paper describes a new nonhydrostatic mesoscaleNWP model at JMA. The model, the JMA nonhydro-static model, has been in operation since 1 September2004. Although the horizontal resolution is 10 km as inMSM at first, the resolution is scheduled to be en-hanced to 5 km in March 2006, and the model is run ona 3-hourly time scale (8 times a day). The forecast timeis scheduled to be extended to 33 h in March 2007 tocover a part of short-range forecast at JMA. Dynamicalprediction of precipitation with a cloud-resolving reso-lution (2 km) that aims at local aviation forecast is alsoplanned.

In section 2, a brief history of the JMA nonhydro-static model is introduced. In section 3, the dynamicalframework is presented. Revisions of physical pro-cesses for a 10-km operational NWP model are de-scribed in section 4. Verification of the model is pre-sented in section 5. Summary and concluding remarksare given in section 6.

2. Overview of the JMA nonhydrostatic model

The JMA nonhydrostatic model (NHM) is a commu-nity model for operation and research. The originalroot is the nonhydrostatic model developed at the Fore-cast Research Department of the Meteorological Re-search Institute (MRI; Ikawa and Saito 1991). Ikawaand Saito’s model was initially developed as a researchtool while it was modified to a nesting model (Saito1994) to realistically simulate mesoscale phenomena.The basic equations were rewritten from the originalanelastic equations to fully compressible equations in-cluding a map factor (Saito 1997) where the lineariza-tion using the reference atmosphere was removed. Thesemi-implicit time-integration scheme [horizontally im-plicit–vertically implicit (HI-VI) scheme] was em-ployed. Furthermore, the modified centered differenceadvection scheme (Kato 1998), and atmospheric radia-

tion schemes (Kato 1999; Eito et al. 1999), etc., werealso incorporated into the model. These modificationsextended the model to a full-scale mesoscale modelcalled MRI-NHM (Saito and Kato 1999), which wasused for several studies at MRI (e.g., Fujibe et al. 1999;Seko et al. 1999; Saito et al. 2001b).

In 1999, a cooperative effort to develop a communitymodel for NWP and research started between the Nu-merical Prediction Division (NPD) and MRI. As thefirst step, the split explicit scheme [horizontally explic-it–vertically implicit (HE-VI) scheme] was reincorpo-rated into MRI-NHM by Muroi et al. (1999), consider-ing the computational efficiency in the parallel comput-ing architecture. A unified model, MRI/NPD-NHM,was completed in 2000, and a comprehensive descrip-tion was published as a technical report from MRI(Saito et al. 2001a). Since 2001, development of an op-erational nonhydrostatic mesoscale model has beenmade by NPD and MRI. Several modifications de-scribed in sections 3 and 4 were added to enhance com-putational efficiency, robustness, and accuracy as anoperational NWP model with a horizontal resolution of10 km.

On 1 September 2004, after 5 months of preopera-tional daily trial runs, JMA replaced MSM with a newnonhydrostatic model (JMA-NHM, hereafter referredto simply as NHM). Eighteen-hour forecasts have beenrun 4 times a day to support disaster prevention and thevery short range forecast of precipitation at JMA.Table 1 summarizes the specifications of MSM and theoperational version of NHM. A domain of 3600 km �2880 km, which covers Japan and its surrounding area(Fig. 1), is taken. Vertically, 40 levels with variable gridintervals from �z � 40 to �z � 1180 m are employed,where the model top and the lowest level are located at22 060 and 20 m, respectively.

Initial conditions for horizontal wind, temperature,water vapor, and surface pressure are given by the JMAMeso 4DVAR (Ishikawa and Koizumi 2002) analysisevery 6 h as in MSM. To prepare initial conditions ofcloud microphysical quantities, a 6-hourly forecast–forecast cycle system is employed, where cloud micro-physical quantities are given by the 6-h forecast ofNHM (see section 4a). Lateral boundary conditions aresupplied from forecasts of the 20-km resolution Re-gional Spectral Model (RSM) of JMA, while the initialtime of RSM is 6 or 12 h earlier than NHM as in theoperational condition of MSM. After the data cutofftime of 50 min and the 4DVAR analysis of 30 min, the18-h model integration is performed within 25 min andthe forecast results are disseminated to users within 2 hfrom its initial time.

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3. Dynamics and numerical techniques

a. Basic equations

The governing basic equations of NHM consist of thefollowing flux form equations on the spherical curvilin-ear orthogonal coordinate:

�

�t � �u

m2� �

m1

m2

�p�

�x� �Adv1 � R1, �1�

�

�t � ��

m1� �

m2

m1

�p�

�y� �Adv2 � R2, and �2�

�

�t ��w

m3� �

1m3

�p�

�z� �

1m3

��g � Adv3 � R3. �3�

Here, u, v, and w represent velocity components; and p,�, and g represent the pressure, density, and gravityconstants, respectively. Subscripts 1, 2, and 3 corre-spond to components x, y, and z, respectively; and vari-ables with a prime express perturbation from the hy-drostatic reference state (in NHM, horizontal averageof the initial virtual potential temperature field [see(E1-2-1) in Saito et al. (2001a)]. The map factors aredenoted as m1 and m2 for the x and y directions, re-spectively; while m3 is not a map factor in the z direc-tion but a variable introduced for definition of momen-tums. MRI-NPD/NHM assumed the conformal projec-tion; m1 � m2 � m3 � m, while m2 and m3 wereintroduced recently by Yamazaki and Saito (2004) tocope with the cylindrical equidistant projection.1

In the operational version for mesoscale NWP atJMA, the Lambert conformal projection is employed,and the map factors are given by

1 If we take the map factors m1 � (1/a cos), m2 � (1/a), m3 �1, and define horizontal wind components as u � a cos(d/dt),v � a(d/dt), Eqs. (1)–(3) are reduced to the conventional mo-mentum equations in the spherical coordinates (Saito 2001).

FIG. 1. Domain and orography of the operational version ofNHM. Domain size is 3600 km � 2880 km. Contour interval is 500m. Areas higher than 1000 m above sea level are shaded.

TABLE 1. Specifications of MSM and operational version of NHM.

MSM NHM

Horizontal mesh (resolution) 361 � 289 (10 km)

Same as in MSM

Mapping Lambert conformalForecast period 18 hInitial time 0000, 0600, 1200, 1800 UTCData cutoff 50 minInitial conditions Meso 4DVARLateral boundary RSMDynamics Hydrostatic NonhydrostaticPrognostic variables u, v, log p, Tv, qv U, V, W, P, �, qv, qc, qi, qr, qs, qg

Levels 40 p-� hybrid 40 terrain followingModel top 10 hPa 22 060 mHorizontal discretization Double Fourier spectral (Arakawa A) Arakawa CHorizontal advection Spectral method Flux form fourth-order with advection correction and

time splittingGravity waves Semi-implicit Time splittingSound waves — Vertically implicit, horizontally split and explicitMoist physics Large-scale condensation with evaporation Three-ice bulk microphysicsConvection Arakawa–Schubert with moist convective

adjustmentModified Kain–Fritsch scheme

Turbulence Level 2 closure Diagnostic TKE schemeBoundary layer Nonlocal scheme Sun and Chang (1986)Radiation thinning Every 60 min in time Every 15 min in time, 20 km in space


m1 � m2 � m3 � � cos�

cos�1�c�1�1 � sin�1

1 � sin� �c

, �4�

where is the latitude of the concerned point and 1 � /6, and c is given by

c � ln�cos�1

cos�2�� ln� tan��

4�

�1

2 �tan��

4�

�2

2 �� . �5�

When 2 � /3, c is about 0.72. Terms with Adv denotethe advection terms and R the residual terms includingcurvature, Coriolis, and diffusion terms.

In NHM, density is defined by the sum of the massesof moist air and the water substances per unit volume as

� � �d � �� c � �r � �i � �s � �g

� �a � �c � �r � �i � �s � �g, �6�

where subscripts c, r, i, s, and g represent the cloudwater, rain, cloud ice, snow, and graupel, respectively;�d is the density of dry air; and �v is the density of watervapor. The continuity equation is as follows:

��

�t� m1m2� �

�x � �u

m2� �

�

�y � ��

m1��

��w

�z

� prc � �DIF.q� . �7�

Here, we neglected the divergence term due to curva-ture of the earth (�2�w/a, where a is radius of theearth), following the shallow assumption. In the right-hand side, prc is the fallout of the precipitable watersubstances defined by

prc ��

�z��aVrqr � �aVsqs � �aVgqg�, �8�

where V is the terminal velocity and q is the mixingratio of the precipitable water substances. Wacker andHerbert (2003) pointed out that unless the fully bary-centric velocity is utilized, diffusion flux appears in thecontinuity equation. The last (underlined) term in therhs of Eq. (7) is the diffusion of water vapor in unittime, which includes subgrid-scale turbulent mixing andcomputational diffusion. This term has been newlyimplemented by Saito (2004) to consider surface evapo-ration of water vapor for total mass conservation asmentioned in section 3i.

The thermodynamic equation is given by

d�

dt�

��

�t� Adv. � �

Q

Cp�� Dif.�, �9�

where � is the potential temperature, Cp is the specificheat of dry air at constant pressure, and is the Exnerfunction.

The state equation is given as the diagnostic equationfor density as

� �p0

R�m� p

p0�C��Cp

. �10�

where �m is the mass-virtual potential temperature(Saito 1997) defined by

�m � ��1 � 0.608q��1 � qc � qr � qi � qs � qg�. �11�

b. Basic equations in the terrain-followingcoordinate

The basic equations mentioned in the preceding sec-tion are transformed to the terrain-following coordi-nate (Gal-Chen and Somerville 1975)

z* �H�z � zs�

H � zs, �12�

where zs is the surface height, and H is the model-topheight. Applying the chain rules of the coordinatetransformation from (x, y, z) to (x, y, z*), Eqs. (1)–(3)are transformed to

�U

�t�

m1

m2��P

�x�

�G1�2G13P

G1�2�z*� � �ADVU � RU,

�13�

�V

�t�

m2

m1��P

�y�

�G1�2G23P

G1�2�z*� � �ADVV

� RV, and �14�

�W

�t�

1

m3G1�2

�P

�z*�

m3

gP

Cm2 �

1m3

BUOY

� ADVW � RW,

�15�

where G1/2, G1/2G13, and G1/2G23 are metric tensors

G1�2 � 1 �zs

H, G1�2G13 � �z*

H� 1� �zs

�x,

G1�2G23 � �z*H

� 1� �zs

�y, �16�

and U, V, and W are momentum as the prognostic vari-ables:

U ��G1�2u

m2, V �

�G1�2�

m1, W �

�G1�2w

m3. �17�


In the source code of NHM, wind components u, v, andw are treated as the diagnostic variables; P is the per-turbation pressure defined by

P � p�G1�2, �18�

and Cm is the sound wave speed [see Eq. (33)].The buoyancy term is defined by

BUOY � �� gG1�2,

ADVU � m��Uu

�x�

�Vu

�y � ��W*u

�z*�

u

mPRC, �19�

where � is a switching parameter, which takes zero indirect computation of the buoyancy from the densityperturbation and unity in conventional computation bythe temperature perturbation. In the HE-VI version ofMRI/NPD-NHM � � 1 was presumed, while in thelatest version of NHM � � 0 is available for both theHE-VI and HI-VI schemes. As mentioned later in sec-tion 3f, the choice of the value of � is related to con-servation of domain-averaged mean surface pressure.

The advection terms are as follows:

ADVU � m1��Uu

�x�

�Vu

�y � �m3

m2

�W*u

�z*

�U

�G1�2 PRC, �20�

ADVV � m2��U�

�x�

�V�

�y � �m3

m1

�W*�

�z*

�V

�G1�2 PRC, and �21�

ADVW �m1m2

m3��Uw

�x�

�Vw

�y � ��W*w

�z*

�W

�G1�2 PRC. �22�

Here W* is the vertical momentum in the z* coordinatedefined by

W* ��G1�2

m

dz*dt

�1

G1�2 �W � m�G1�2G13U � G1�2G23V��, �23�

and PRC corresponds to the rhs of Eq. (7):

PRC ��

�z*��aVrqr � �aVsqs � �aVgqg�. �24�

Here RU, RV, and RW represent the residual termsincluding the curvature, Coriolis, and diffusion terms:

RU � f3

m1

m2V � f2

m3

m2W � V�u

�m1

�y� ��m1

m2�2 �m2

�x �� U

w

a� DIF.U, �25�

RV � f1

m3

m1W � f3

m2

m1U � U�u�m2

m1�2 �m1

�y� �

�m2

�x �� V

w

a� DIF.V, and �26�

RW � f2

m2

m3U � f1

m1

m3V �

1

m3�G1�2

�m2U�2 � �m1V�2

a

� DIF.W, �27�

where a is the radius of the earth, and the Corioliscoefficients are given by

f1 � �2 cos� sinc��, f2 � 2 cos� cosc��,

f3 � 2 sin�, �28�

respectively. Here, � (� � 0) is the difference be-tween local longitude and standard longitude, the de-flection of the y direction from the north direction.2

The continuity Eq. (7) is rewritten as follows:

G1�2��

�t� DIVT�U, V, W� � PRC, �29�

where DIVT is the total divergence in the z* coordinatedefined by

DIVT�U, V, W� � m2��U

�x�

�V

�y � � m�W*�z*

, �30�

The thermodynamic equation is identical to Eq. (9),while the advection term is given by

Adv.� � �m� �

�x ��u�

m � ��

�y ��

m ��

�z ��w�

m ��

�

m �PRC ��

�t � m

�. �31�

The advection terms for cloud microphysical quantitiesare also given by this formula.

The state equation is the same as in Eq. (10), and thepressure equation is obtained from Eqs. (10) and (29) as

2 Inclusion of the full Coriolis and curvature terms with theshallow assumption does not possess the conservation of the an-gular momentum (Phillips 1966; White and Bromley 1995). In theoperational version, terms relating to f1, f2, and 1/a in (25)–(27)are omitted as is the common manner in hydrostatic NWP models.This approximation does not change the forecast of mesoscalephenomena.


d�

dt�

Q

CP�� DIF.�, �32�

where Cm is given by

Cm2 �

Cp

C�

R�m� p

p0�R�Cp

, �33�

and PFT is the local time tendency of the mass-virtualpotential temperature,

PFT ��G1�2

�m

��m

�t. �34�

In case of no water substances, Cm corresponds tosound wave speed. In the sponge layer near lateral andupper boundaries, a term of Rayleigh damping for pres-sure is added to the rhs of Eq. (32).

c. Finite discretization

The model grid structure is the Arakawa C type inthe horizontal direction and the Lorenz type in the ver-tical direction, which is the same as in MRI/NPD-NHM. The detailed structures of the staggered grid aredescribed in section D-1 of Saito et al. (2001a). InNHM, to avoid interpolation and save the computationtime, map factors are computed not only at scalarpoints but also at vector (u and v) points in advance.

A higher-order (from third to fifth) advectionscheme that considers staggered grid configuration hasbeen implemented by Fujita (2003). In the operationalforecasting at JMA, the fourth-order scheme is chosen,considering computational cost and matching with theadvection correction scheme mentioned later. Thefourth-order finite difference for gradient is expressedby

��

�xi�4�

�98

�i�1�2 � �i�1�2

x�

18

�i�3�2 � �i�3�2

3 x

�3

640� x�4��5� � O�� x�6�. �35�

Comparing with the conventional fourth-order finitedifference for unstaggered system (e.g., Xue et al. 1995)

��

�xi�4�

�43

�i�1 � �i�1

2 x�

13

�i�2 � �i�2

4 x�

130

� x�4��5�

� O�� x�6�, �36�

the cutoff error in Eq. (35) is about 1/7.3

For advection of scalar prognostic variables, thefourth-order finite difference for a flux form gradientterm that appeared in Eq. (31) is given by4

�U�

�x i�4�

�98

�U�x�i�1�2 � �U�

x�i�1�2

x

�18

�U�x�i�3�2 � �U�

x�i�3�2

3 x, �37�

where

� i�1�2x

�9

16��i�1 � �i� �

116

��i�2 � �i�1�. �38�

The above-mentioned higher-order schemes are em-ployed jointly with the modified centered differenceadvection scheme (Kato 1998). This scheme is a kind offlux limiter and acts as the flux correction scheme. Itmodifies the advection terms to remove numerical er-rors due to the finite-difference approximation and toassure the monotonicity.

d. Basic formulation of HE-VI scheme

The time-splitting, horizontally explicit, and verti-cally implicit (HE-VI) scheme is used in the operationalversion of NHM. The basic formulation of the HE-VIscheme of MRI/NPD-NHM was reimplemented byMuroi et al. (1999) with reference to the HE-VI versionof Ikawa and Saito (1991), where only sound waveswere treated implicitly as the high-frequency modebased on Klemp and Wilhelmson (1978).

For horizontal momentum Eqs. (13) and (14), theforward time integrations

U�� U�

��

m1

m2��P�

�x�

�G1�2G13P�

G1�2�z*�

� ��ADVU � RU�, �39�

V�� V�

��

m2

m1��P�

�y�

�G1�2G23P�

G1�2�z*�

� ��ADVV � RV� �40�

3 In a similar manner, the third-order and fifth-order schemesare defined by (��/�x)|(3)

i � (1/12)(9�i�1/2 � 8�i � 18�i�1/2 ��i�3/2/�x), and (��/�x)|(5)

i � (1/960)(�25�i�3/2 � 900�i�1/2 �384�i � 1350�i�1/2 � 100�i�3/2 � 9�i�5/2/�x), respectively.

4 The Weather Research and Forecasting model developed atthe National Center for Atmospheric Research (NCAR-WRF)uses a cell-interface-based difference scheme. For a fourth-orderscheme, the gradient term is written by (�U�/�x) � {Ui�1/2[7(�i�1

� �i) � (�i�2 � �i�1)] � Ui�1/2[7(�i � �i�1) � (�i�1 � �i�2)]/12�x}.This formulation guarantees high-order accuracy when U is con-stant and is easier for parallelization and boundary treatment.


are used, and the backward time integration is em-ployed for vertical momentum Eq. (15):

W�� W�

��

1

m3G1�2

�P�

�z*�

g

m3Cm2 P�

�1

m3BUOY � �ADVW � RW� � �1 � �

g

m3Cm2 P�,

�41�

where

P� �1 � �

2P��

1 � �

2P�. �42�

In the HE-VI scheme of MRI/NPD-NHM � � 1 wasassumed, while � � 0 can be used in the latest versionof NHM (Saito 2004) to improve the mass conservationas mentioned in section 3f. Note that the last term in lhsof Eq. (41) appears independent of the value of �, andthe last term in rhs is introduced for stability to treat thesound waves mode in the buoyancy term implicitlywhen � � 0 (see footnote 5).

e. Divergence damping

To attenuate computational instability of soundwaves in the HE-VI time integration scheme, an acous-tic filter has been introduced to NHM. Although the

idea is based on Skamarock and Klemp (1992), thedamping terms act on the flux form total divergence(DIVT); thus, the formulation is slightly different fromSkamarock and Klemp’s (1992) acoustic filter em-ployed in advective form basic equations. The followingunderlined terms are added to the residual terms of Eqs.(13)–(15) only for the HE-VI scheme:

RU → RU � �H

m1

m2� �

�x�

�G1�2G13

G1�2�z*�DIVT, �43�

RV → RV � �H

m2

m1� �

�y�

�G1�2G23

G1�2�z*�DIVT, �44�

RW → RW ��

G1�2�z*�ZDIVT, �45�

where coefficients �H and �Z are set to about one-fourth of the maximum values that allow the linearstable condition for diffusion,

�H � 0.061 t

min�� x

m1�2

, � y

m2�2�, �46�

�V � 0.051 t

�G1�2 z�2. �47�

f. Pressure equation

Pressure Eq. (32) is integrated backward as

P�� P�

�� Cm

2 ��PFT � m1m2��U�

�x�

�V�

�y � � m3

�

�z* � 1

G1�2 �W� �m1m2

m3�G1�2G13U� � G1�2G23V��

� PRC� � DIF.P, �48�

where DIF.P is a term of Rayleigh damping for pres-sure, and the definition of U� and V� is the same as inEq. (42).

Eliminating U�, V�, and W� by Eqs. (39)–(42) withthe same manner as described in (C-3-2) of Saito etal. (2001a), we obtain the following one-dimensionalHelmholtz-type pressure equation:

�2P�

�z*2 � G1�2�

�z* � g

Cm2 P�� G1�2�2� 2

Cm ��1 � ��2

P�

� FP.HE.INV � FP.HE.VAR, �49�

where FP.HE.INV is the invariant term during shorttime step integration in the forcing terms,

FP.HE.INV � �2�G1�2�2

��1 � �� PFT � PRC �DIF.P

Cm2 �

� G1�2�

�z*�BUOY � m3�ADVW � RW�

�g

Cm2 P�, �50�

and FP.HE.VAR is the variable term during short timestep integration in the forcing terms

FP.HE.VAR �2�G1�2�2

��1 � ��m1m2DIVH�U�, V��

�m3

G1�2

�W�

�z*�� 2G1�2

Cm ��1 � ��2

P�.

�51�


Here, DIVH stands for horizontal divergence

DIVH�U, V� ��U

�x�

�V

�y�

�

�z*�G13U � G23V�. �52�

The upper boundary condition is obtained from �W �0 as

� 1

m3G1�2

�

�z*�

g

m3Cm2 �P�

� ��ADVW � RW� �1

m3�BUOY � �1 � �

g

Cm2 P�.

�53�

The lower boundary condition is the same as in Eq.(53), while in free-slip case, we should add the followingextra term to the rhs:

1 � �W� �

m1m2

m3�G1�2G13U�� G1�2G23V�� .

�54�

The upper (and lower) boundary condition [Eq. (53)]needs values of pressure at upper and lower boundariesbecause it includes a pressure perturbation term (gP�/m3C2

m) in the lhs. To determine this term, we need pres-sure values at kz � 1 and nz, since upper and lowerboundaries are defined at kz � 1 � 1/2 and nz � 1/2 asin the level of W. The one-dimensional elliptic pressureEq. (49) gives solutions of pressure only for the levelsfrom kz � 2 to nz � 1; thus, determination of pressurevalues at upper and lower boundaries is influential tothe inside solution, and a simple extrapolation some-times deteriorates the mass conservation. To preventthis problem, we compute the buoyancy by density per-turbation choosing � � 0 in Eq. (19), so that the pres-sure perturbation term (gP�/m3C2

m) in the lhs of Eq.(53) almost offsets5 the last term of the rhs (gP/m3C2

m)and determination of this term becomes less crucial.

Figure 2 shows the time sequences of domain-averaged mean sea level (MSL) pressure from by NHMwith � � 1 and � � 0. In this experiment, the initialcondition is the Meso 4DVAR analysis at 0600 UTC 1March 2003, and the boundary condition is supplied byRSM. In this case, the MSL pressure of RSM decreaseswith time and becomes 1009.6 hPa at forecast time (FT)� 18. However, when � � 1, MSL pressure of NHMincreases about 0.5 hPa at startup, and becomes 1010.8hPa at FT � 18, which is 1.2 hPa higher than that of

RSM. This discrepancy results in a high MSL pressurebias. By choosing � � 0 (operational choice), the initialrise of MSL pressure of NHM is removed and averagedpressure follows well that of the parent model (RSM).

g. Time splitting of gravity waves

In the HE-VI scheme shown in section 3d, onlysound waves are treated implicitly as the high-frequency mode. However, in operational NWP, grav-ity waves often affect computational efficiency and ro-bustness. A time-splitting scheme of gravity waves hasbeen implemented by Saito (2002). To split gravitywaves, thermodynamic Eq. (9) may be written as fol-lows, evaluating the vertical advection of the potentialtemperature in the reference state in short time step:

��

�� w�

N2�

g� w

��

�z� u

��

�x� �

��

�y��

Q

cp�� DIF.�. �55�

However, the advection term of NHM is written in fluxform Eq. (31), and advection correction is implementedas mentioned in section 3c. To use the finite-differenceform of advection of potential temperature in NHM asit is, we modify Eq. (55) as

��

�� w�

d�

dz� w

��

�z� u

��

�x� �

��

�y��

Q

cp�� DIF.�,

� ��d�

dz�w� � w� � Adv.��

Q

cp�

� DIF.�,

� �d�

dz�w� � w� � ��

�t �. �56�

5 Needless to say, a simple implicit treatment of the verticalmomentum equation (W�� W�/��) � (1/m3G1/2)(�P�/�z*) �(1/m3)BUOY � ADVW � RW causes computational instabilityof sound waves because the buoyancy term includes pressure per-turbation if we take � � 0.

FIG. 2. Time sequences of the mean sea level pressure by NHMand RSM. Domain-averaged values for area of MSM are shown.Initial time is 0600 UTC 1 Mar 2003.


Here, the last term in the rhs of Eq. (56) is given by atentative integration in cloud microphysics, and the firstterm is evaluated by first-order upstream difference.Since the tentative integration is done with high-orderflux form, the conservative property of flux form is keptin the limit, where w� in the short time step agrees withw at the long time step.

h. Time split of advection

The above-mentioned time splitting of gravity wavesworks in most cases; however, we faced computationalinstability in some cases where environmental wind isstrong and a strong inversion layer exists. To overcomethis problem a new time-splitting scheme of advection(Saito 2003) has been developed.

Hsu and Sun (2001) proposed a time-splitting schemeof advection in their forward scheme model. It is ex-pected that computing advection terms in short timestep �� contribute to improve the computational sta-bility. However, this choice is not acceptable becausethe higher-order advection scheme with the modifiedadvection scheme is computationally expensive andspoils the computational efficiency of the HE-VIscheme. In fact, a simple application of computation ofadvection to each short time step is not so effective inthe leapfrog scheme, because such application changesthe leapfrog scheme from centered base to forwardbase in time.

In the new splitting scheme, we fully evaluate higher-order advection terms with the modified advectionscheme at the center of the leapfrog time step, and thenadjust the lower-order (second order) components ateach short time step only in the latter half of the leap-frog time integration as shown in Fig. 3,

ADV � ADV�kt� � ADVL�kt� � ADVL�. �57�

Here, ADV(kt) is the higher-order advection withthe modified advection scheme at time step kt, whileADVL(kt) and ADVL� are the lower-order advectioncomponent at kt and each short time step ��, respec-tively. This adjustment is done from (ns � 1)/2 � 1 tons � 1, where ns is the ratio of 2�t and ��.

To treat sound waves implicitly and split the gravitywaves, the vertical momentum equation is rewritten as

W�� W�

��

1

m3G1�2

�P�

�z*�

g

m3Cm2 P�

�1

m3BUOY�� ADVW � ADVLW � ADVLW�

� RW� � �1 � �g

mCm3

2 P�. �58�

The time splitting of advection of potential temperatureis an alternative way to split gravity waves:

��

�� Adv.� � ADVL� � ADVL��

�Q

cp�� DIF.�,

� ADVL� � ADVL��

�t �. �59�

Here ADVL� is computed by a flux form second-ordercentral difference. In the operational version of NHM,Eq. (59) is used instead of Eq. (56) for simplicity andeconomy for 10-km-resolution runs. As mentioned inthe former subsection, the last term of the rhs of Eq.(59) is given by tentative time integration in the cloudmicrophysical process.

Figures 4a and 4b show vertical cross sections of po-tential temperature and vertical wind at 0600 UTC 9April 2002 as a case of computational instability ofNHM. Computational domain and specifications arethe same as in the operational version of NHM de-scribed in section 4a. In this case, a strong inversionlayer existed at the 9-km level above the northeasternpart of China, with strong horizontal wind. A compu-tational instability occurred with �t � 40 s without timesplitting of advection. Figures 4c and 4d are corre-sponding results when advection terms are split. In thiscase, short time step �� is 11.4 s, and modification ofadvection is conducted 3 times per single large timestep integration.

The time-splitting scheme mentioned above and thedivergence damping enables NHM to use 40 s for �t inthe leapfrog scheme to realize a stable run with a hori-zontal resolution of 10 km, which corresponds to 80 sin the second-order Runge–Kutta time-integrationscheme.

Table 2 shows comparison of computational times ofthe 2-h run for the domain of the operational meso-scale prediction (361 � 289 � 40) with two nodes ofHITACHI SR8000F1. Three cases, (a) no time splittingwith �t � 20 s, (b) time splitting of gravity waves with

FIG. 3. Time splitting of advection for case of ns � 2�t/�� 7.


FIG. 4. East–west vertical cross section of NHM forecast for 0900 UTC 9 Apr 2002. Initial time is 0600UTC 9 Apr 2002; �t � 40 s, �� 11.4 s, and only gravity waves are split by Eq. (58). (a) Potentialtemperature; contour interval is 5 K. (b) Vertical wind; contour interval is 5 cm s�1. (c), (d) Same as (a),(b) but advection terms are split.


�t � 30 s, and (c) time splitting of advection with �t �40 s, are compared using almost the same specificationsas in the operational run. In this table, all computationsincluding time splitting of advection in short time stepsare accounted for as “short-step dynamics.” By splittinggravity waves, the number of long time steps decreasesto 2/3 and total computation time decreases to 74%.When the long time step is set to 40 s with time splittingof advection, number of long time steps decreases to 1/2and total computation time decreases to 61%. Since com-putation in short-step dynamics increases for the time-splitting treatment and the radiation process is consid-ered every 15 min, the total computation time is not indirect proportion to the number of large time steps; stillthese time-splitting schemes for gravity waves and ad-vection considerably improve the model efficiency.

i. Lateral boundary condition and flux adjustment

Rayleigh damping sponge layers, which enforce theexternal values on the prognostic variables, are im-posed near the lateral boundaries. In MRI/NPD-NHM,Rayleigh damping is employed for momentum, pres-sure, and potential temperature, while in current NHM,Rayleigh damping is used for specific humidity as well.

To satisfy the relation between time tendency of thetotal mass within the entire model domain and the totalmass flux through the lateral boundaries, a flux adjust-ment scheme at lateral boundaries is employed. Vol-ume integrating the continuity Eq. (29), we obtain thefollowing relation between the time tendency of thetotal mass in the entire model domain and the mass fluxthrough the lateral boundaries:

�

�t ��G1�2

m2 dx dy dz * � ��U dy dz *�x�0

� ��U dy dz *�x�X

� ��V dx dz *�y�0

� ��V dx dz *�y�Y

� �� 1m1m2

��PRC� � �q��w��*z�0dx dy. �60�

The last term in the above equation represents a dif-ference between the area mean precipitation rate andthe total surface flux of water vapor (total evaporationat surface). Since these terms offset each other, themagnitude of the adjustment for the mass flux at lateralboundaries decreases by the inclusion of the diffusionterm of moisture in the continuity equation.

j. Code parallelization

The code parallelization is an important issue forNWP models in current computer architectures. Re-

cently, an option of two-dimensional decompositionhas been implemented in NHM (Aranami and Ishida2004). Generally, the two-dimensional decompositionmakes each communication length between computa-tional nodes shorter and the load balance among com-putational nodes could become better. However, theincrease of the communication frequency brings aboutmore overhead for communication and the reduction ofeach loop length may lead to inefficiency in computa-tion. Either one- or two-dimensional decompositionscan be chosen for NHM so that the computational ef-ficiency becomes best in accordance with the architec-

TABLE 2. Computational time for 2-h run for MSM domain (361 � 289 � 40).

(a) No time splitting�t � 20 s

(b) Time splitting ofgravity waves �t � 30 s

(c) Time splitting ofadvection �t � 40 s

CPU (s) ( ) CPU (s) ( ) CPU (s) ( )

Initial setting 97.5 3.7 102.2 5.1 104.2 6.4Diagnosis 50.8 2.0 33.2 1.7 24.5 1.5Advection 283.3 10.6 187.4 9.5 141.4 8.7Short-step dynamics 208.8 7.9 348.7 17.7 358.2 22.1Surface stress 87.8 3.2 55.5 2.8 41.7 2.6Radiation 62.8 2.4 53.3 2.7 46.3 2.9TKE and diffusion 121.0 4.4 80.3 4.0 60.6 3.7Cloud microphysics 1694.5 63.7 1076.9 54.5 812.3 50.2Others 64.7 2.0 37.9 1.9 29.9 1.8Total 2659.2 100 1975.6 100 1619.6 100Acceleration (%) 100 74.2 60.9


ture of the hardware, the number of available compu-tational nodes, and the problem size.

Writing output of the computed results on disks oftenconsumes substantial elapsed time in parallel comput-ing. A special node can be exclusively spared for theoutput process on user’s demand in the parallel com-putation of NHM. A set of “fake MPI” subroutines isoffered for users who use NHM on personal computerswithout the MPI libraries.

4. Physical processes

a. Cloud microphysics

An explicit three-ice bulk microphysics scheme(Ikawa and Saito 1991) based on Lin et al. (1983) isincorporated. The pressure perturbation term was lin-earized to compute temperature perturbation in MRI/NPD-NHM, but this approximation has been removedin the latest version of NHM. Although the original fullmicrophysics predicts number concentrations of cloud,snow, and graupel, only mixing ratios are treated as theprognostic values in the operational version. Besides,an economical, reduced version of the bulk method hasbeen developed by Yamada (2003a), where some trivialterms mainly for production of graupel are omitted(Fig. 5; see Table 3 for list of symbols used in Fig. 5). As

FIG. 5. Cloud microphysics of NHM. Variables and processes inshadowed squares are omitted in the operational version of NHM.For list of symbols, see Table 3.

TABLE 3. List of symbols in Fig. 5.

Notation Description

Ni Number concentration of cloud iceNs Number concentration of snowNg Number concentration of graupelPccnd Production of cloud water by condensation of water

vaporPccnr Generation of rain by collision and coalescence of

cloud waterPgaci Production of graupel through accretion of cloud

ice by graupelPgacr Production of graupel through accretion of rain by

graupelPgacs Production of graupel through accretion of snow by

graupelPgacw Production of graupel through accretion of cloud

water by graupelPgdep Production of graupel for depositional growthPgfzr Production of graupel by probabilistic freezing of

rainPg.iacw Production of graupel through accretion of cloud

water by cloud icePg.racs Production of graupel through accretion of snow by

rainPg.sacr Production of graupel through accretion of rain by

snowPg.sacw Production of graupel through accretion of cloud

water by snowPgmlt Production of rain by melting of graupelPgprc Precipitation of graupelPiacr Production of graupel through accretion of rain by

cloud icePicng Generation of graupel through accretion of rain by

cloud icePicns Generation of snow by conversion of cloud icePidep Production of cloud ice by depositional growth of

cloud icePidsn Generation of cloud ice by nucleation of cloud icePifzc Production of cloud ice by freezing of cloud waterPi.iacw Production of cloud ice through accretion of cloud

water by cloud icePimlt Production of cloud water by melting of cloud icePispl Production of cloud ice by ice splinter multiplicationPraci Production of graupel through accretion of rain by

cloud icePracs Production of snow through accretion of snow by

rainPracw Production of rain through accretion of cloud water

by rainPrevp Production of water vapor by evaporation of rainPrprc Precipitation of rainPsaci Production of snow through accretion of cloud ice

by snowPscng Generation of graupel by rimming of snowPsdep Production of snow by depositional growthPsmlt Production of rain by melting of snowPs.sacr Production of snow through accretion of rain by

snowPs.sacw Production of snow through accretion of cloud water

by snowPsprc Precipitation of snow


an additional tuning for operation, evaporation rates ofrain, snow, and graupel are modified to 50% of theoriginal rates to reduce excessive evaporation in thelower atmosphere found in 10-km-resolution runs. Be-sides, Kessler’s autoconversion threshold value fromcloud water to rain is modified from the original valueof 1 to 0.1 g Kg�1 to avoid the underestimation of weakprecipitation.

The box-Lagrangian scheme (Kato 1995) is appliednot only to computation of fallout of rain but also tograupel to keep computational stability for �t � 40 s inoperation.

To prepare initial conditions of cloud microphysicalquantities, a 6-hourly forecast–forecast cycle system isemployed, where cloud microphysical quantities aregiven by the 6-h forecast of NHM but set to zero at thegrid points where the relative humidity is less than 90%(Ishida and Saito 2005). Figure 6 shows the time se-quences of numbers of grid points where precipitationintensity exceeds threshold values in a simulation of0000 UTC 11 November 2003. Without the forecast–forecast cycle of cloud microphysical quantities, pre-cipitation of NHM is too weak at initial startup. At thefirst 1 h, the numbers of grid points are less than half ofthose of MSM. This underestimation of rain affects sub-sequent forecasts of NHM up to 6 h. With the forecast–forecast cycle of cloud microphysical quantities, this un-derestimation is ameliorated.

b. Convective parameterization

Cumulus parameterization is one of the most im-portant issues to determine model performance inGCM and NWP models. Although MRI/NPD-NHMwas equipped with two convective parameterizationschemes (the Arakawa–Schubert scheme and themoist convective adjustment scheme), performanceof these schemes are not ensured in a relatively highhorizontal resolution such as 10 km, because theseschemes were originally developed for GCMs, assum-ing that horizontal grid space is much lager than thecloud scale.

In NHM, the Kain–Fritsch (K-F) convective param-eterization scheme (Kain and Fritsch 1993) has beenimplemented by Yamada (2003b). In addition to therecent modifications described in Kain (2004), sev-eral points have been revised by Ohmori and Yamada(2004) to improve its performance with a 10-kmresolution for prediction of heavy rainfall events in Ja-pan, where a moist and unstable maritime air mass pre-vails.

In the “trigger function” in the Kain–Fritsch scheme,a concept of temperature increment is introduced tosimulate local perturbation forcing as a function of grid-scale updraft. Even though this temperature incrementis formulated in the original scheme as a function ofhorizontal resolution, the original scheme sometimes

FIG. 6. Time sequences of number of grid points exceeding threshold of precipitationintensity. Initial time is 0000 UTC 11 Nov 2003.


produced excessive orographic rainfall. Thus, the factorof an offset (increase) of the airmass temperature at thelifting condensation level was reduced from the originalvalue (1 K) to 0.2 K. To prevent the overestimation of

the grid-scale motion, the updraft at each grid point isevaluated by averaging the values in the adjacent ninegrid points.

As for the calculation of “updraft property,” in the

FIG. 7. (a) Three-hour-accumulated precipitation (mm) at 0000 UTC 19 Jul 2003 by Radar-AMeDAS analysis.(b) Forecast of NHM with the original Kain–Fritsch scheme. Initial time is 0600 UTC 18 Jul 2003. (c) Same as in(a), but with the modified Kain–Fritsch scheme. (d)–(f) Same as in (a)–(c), but at 1800 UTC 19 Jul 2003. Initial timeof NHM is 0600 UTC 19 Jul 2003.


original precipitation formation scheme using Oguraand Cho (1973), precipitation is produced in the up-draft regions regardless of the magnitude of conden-sates. With this scheme, unnatural precipitation pat-terns were sometimes obtained such as elongatedprecipitation regions whose orientations were perpen-dicular to major rainbands. Similar unnatural precipi-tation patterns in the simulation of rainbands with theKain–Fritsch scheme have been reported by Knievel(2002) and H. Kusaka (2004, personal communication).To ameliorate such precipitation patterns, a newscheme based on the concept of the Kessler-type auto-conversion was introduced, in which the parameterizedcondensates in the updraft are converted into precipi-tation only when their values exceed a prescribedthreshold value (1.0 g kg�1).

Concerning the “closure assumption,” the defaultsetting assumed that the convection consumes the pre-existing CAPE by 90% in a single application of the

Kain–Fritsch scheme. However, forecast experimentsshowed that this setting tended to overstabilize themodel atmosphere, and strong rain decreased with timein the forecast period of 18 h. To prevent this undesir-able excessive stabilization of the model atmosphere,the reduction rate of CAPE in the column by a singleapplication of the K-F scheme was diminished from thedefault value (90%) to 85%.

Figure 7 shows an example of the prediction with theoriginal and modified K-F schemes for a heavy rainevent at Kyushu, western Japan, in 2003. At 0000 UTC19 July, heavy rainfall was observed at northern part ofKyushu Island, associated with a major rainband thatruns from the East China Sea to east-northeast (Fig.7a). Figures 7b and 7c show the corresponding simula-tions by NHM whose initial time is 0600 UTC 18 July(FT � 18). In the original K-F scheme, the simulatedrain intensity was relatively weak, and the intense rain-fall was mainly simulated northeast of Kyushu. Unnatu-ral orographic rainfall appeared over the southern partof Kyushu (Fig. 7b). On the other hand, with the re-vised K-F scheme, these shortcomings are amelioratedand the location of the heavy rainfall is improved(Fig. 7c).

This rainband moved southeastward slowly andbrought another heavy rainfall the day after. At1800 UTC 19 July, a heavy rainfall was observed atwestern central part of Kyushu (Fig. 7d). Figures 6e and6f show the corresponding simulations by NHM, whoseinitial time is 0600 UTC 19 July (FT � 12). In theoriginal K-F scheme, the intense rainfall was simulatedin northern part of Kyushu (Fig. 5e), while the locationis much improved with the revised K-F scheme(Fig. 5f).

c. Targeted moisture diffusion

With the above-mentioned modification of the K-Fscheme, representation of heavy rainfall events byNHM was improved. However, intense grid-scale up-drafts often developed in the model with the increasedrate of residual CAPE, because this change allowsmore convective unstableness in the model atmo-sphere.

To control the gridpoint storms and the associatedintense grid-scale precipitation, the targeted moisturediffusion (TMD) has been implemented to NHM (Saitoand Ishida 2005). The basic idea of TMD was devel-oped by T. Davies of the Met Office for the UnifiedModel (Davies et al. 2005), where a second-order hori-zontal diffusion is applied to water vapor when strongupward motions exist to selectively damp the gridpointstorms caused by the positive feedback of the latent

FIG. 8. (a) Time sequences of the maximum updraft in a simu-lation with and without the target moisture diffusion. Initial timeis 1800 UTC 18 Jul 2004. Unit of vertical axis is m s�1. (b) Sameas in (a) but the maximum 1-h rain intensity. Unit of vertical axisis mm h�1.


heat release by condensation and updraft accelera-tion. In the mesoscale UM with 38 levels and a hori-zontal resolution of 0.11° (12 km), TMD is applied to allgrid points in a column where the upward motion ex-ceeds 1.0 m s�1. In case of NHM, horizontal diffusionwith an e-folding time of 300 s is applied to watervapor at grid points where the upward motion exceeds2.0 m s�1.

Figure 8 shows an example of the time sequences ofthe maximum updraft and rainfall intensity by NHM,which covers the domain of the operational mesoscaleprediction. The initial time is 1800 UTC 18 July 2003.Without TMD, the maximum updraft reaches 6 m s�1

at FT � 5–8 h, and very intense rainfalls of about 140mm h�1 at maximum are predicted at FT � 7–8 h. AtFT � 16.8 h, a spikelike strong updraft of 8 m s�1 isseen, which is caused by gridpoint deep convection.With TMD, the maximum updraft and the maximumrain intensity are reduced to reasonable values, lessthan 4.5 m s�1 and 80 mm h�1, respectively.

d. Surface processes

It was known that MRI-NPD/NHM had problems inthe surface properties: the cold bias at the surface incase of unstable conditions, and the wet bias at thesurface. Overestimation of the surface latent heat fluxwas a main cause of the above biases. The followingmodifications have been made by Kumagai (2004a):

1) The value of scalar roughness lengths for heat andmoisture (z0h) has been reduced to about 1/7.4 ofmomentum roughness length (z0m) following Gar-ratt and Francey (1978). This modification reducesthe latent heat flux at surface.

2) Computation of bulk coefficients for surface fluxesover land has been changed from Sommeria (1976)to Louis et al. (1982) as in MSM. This modificationreduces the overestimation of surface fluxes instrongly stable case.

The surface bulk coefficients for momentum (Cdm)and heat (Cdh) fluxes are given by following formula:

Cdm ��am

2 �1

1 �2bRiB

�1 � dRiB : RiB � 0

am2 �1 �

2bRiB

1 � 3bam2 c� za

z0m|RiB| : RiB � 0,

�61�

Cdh � �amah� 1

1 � 3bRiB�1 � dRiB� : RiB � 0

amah�1 �3bRiB

1 � 3bamahc�za

z0|RiB| : RiB � 0,

�62�

where RiB is the bulk Richardson number defined by

RiB �gza

�s

�a � �s

ua2 � �a

2 , and �63�

am ��

logza

z0m

, ah ��

logza

z0h

. �64�

Here, b � c � d � 5, and � (� 0.4) is the von Kármánconstant. Subscripts a and s denote values at the lowestlevel of the model (za � 20 m) and surface, respectively.

3) Following MSM, a stomatal resistance has been in-troduced to express the diurnal and seasonal

changes of the evapotranspiration at the surface.The surface water vapor flux is parameterized by thedownward shortwave radiation flux S↓ as

q��w� � �1

1

Cdq�ua2 � �a

2� rs

�Q�a � q�s�, �65�

rs � rs,day �rs,night

1 �S↓

S0

, �66�

where rs is the stomatal resistance and S0 � 1 Wm�2. In the daytime rs approaches rs,day (30 s m�1

from April to October and 60 s m�1 in other


months), while at night rs becomes rs,day � rs,night

(300 s m�1). The above parameterization reducesthe latent heat flux and ameliorates the excessivemoistening at the lowest level.

e. Boundary layer processes

The above-mentioned wet bias at surface is alsocaused by weak diffusion in the planetary boundarylayer (PBL) of NHM. This tendency also yields weakbias of surface wind. To consider the nonlocal effect,the following modifications have been made by Kuma-gai (2004b):

1) The mixing length in the original version of NHMwas determined by a typical grid interval �s and thelocal atmospheric stability according to Deardorff’s(1980) formula and was modified by Blackadar(1962) near surface so that the mixing length ap-proaches a product of the von Kármán constant andthe height above ground level. However, this treat-ment tended to underestimate the mixing lengthnear surface and suppress the development of con-vective boundary layer. In new NHM, following Sunand Chang (1986), the vertical mixing length lz in theTKE equation is determined using a PBL height hPBL:

lz � �lSC�z� : z � hPBL

max�lSC�hPBL�

1.2 �z

hPBL

0.2, s� : hPBL � z � 1.2hPBL, N2 � 0

max�lSC�hPBL�

1.2 �z

hPBL

0.2, min� s, 0.76

E1�2

N �� : hPBL � z � 1.2hPBL, N2 � 0,

s : z � 1.2hPBL, N2 � 0

min� s, 0.76E1�2

N � : z � 1.2hPBL, N2 � 0

�67�

where E is the turbulent kinetic energy and N is theBrunt–Vaisala frequency, and

lSC�z� � 0.25�1.8hPBL�1 � exp��4z

hPBL�

� 0.0003 exp�8z

hPBL��. �68�

The PBL height is defined by the level at which thevirtual potential temperature exceeds the value atthe lowest level.

2) Anisotropy of turbulence is considered, where themixing lengths are determined separately in the ver-tical and horizontal directions using the vertical andhorizontal grid interval, respectively. The turbulentPrandtl number and turbulent diffusion coefficientsare also determined separately in the vertical andhorizontal directions using the vertical and horizon-tal mixing length, respectively.

f. Diagnosis of turbulent energy

A 1.5-order turbulent closure model is incorporatedin NHM to determine the diffusion coefficients. Thisscheme treats the TKE as a prognostic variable and

integrates the TKE equation. In the TKE prognosticscheme, the initial and lateral boundary conditions ofTKE are required to maintain the structure of theboundary layer; however, these conditions are not sup-plied by the Meso 4DVAR and RSM. Besides, timeintegration of TKE is computationally expensive if weuse a higher-order scheme with the modified advectionscheme. In NHM, when the surface wind is strong, thecomputational mode sometimes appears in the 10-kmrun with �t � 40 s if TKE is computed using a simplefourth-order centered difference scheme without theadvection correction scheme.

To overcome the above problem, a new option hasbeen implemented (Kumagai and Saito 2004), in whichTKE is not predicted but diagnosed. Assuming localequilibrium in the TKE equation, we obtain the follow-ing relation between the buoyancy and shear produc-tion terms and viscosity dissipation term:

�gKhz

�

��

�z*� �

i,jKmj��ui

�xj�

�uj

�xi� �ui

�xj�

Ce

lz�Kmz

Cmlz�3

� 0. �69�

Here, Kmz and Khz are vertical diffusion coefficients formomentum and heat, respectively, and using the verti-


cal mixing length and the inverse turbulent Prandtlnumber, they are given by

Kmz � CmlzE1�2, �70�

Khz � Prz�1Kmz, �71�

Prz�1 �

1

1 � 2lz

z

. �72�

Using Eqs. (69) and (71), Kmz can be obtained by

Kmz2 �

Cm3

Celz4��

i,j

ljlz ��ui

�xj�

�uj

�xi� �ui

�xj�

g

�Prz

�1��

�z*�,

�73�

and turbulent energy is diagnosed by Eq. (70).

g. Implicit treatment of vertical diffusion

In MRI/NPD-NHM, vertical diffusion was treatedexplicitly, where a limiter of diffusion coefficients,

K � Kmax�z� � 0.1� z�2

t, �74�

was imposed to meet the linear stability condition.When a large �t was taken, this limiter restricted thevertical diffusion near the surface, which sometimescaused wet and cooling biases of MRI/NPD-NHM. Im-plicit treatment of vertical diffusion, which was onceimplemented to MRI-NHM by Fujibe et al. (1999), hasbeen reimplemented to NHM. The prognostic equationfor � is discretized in time as

� t� t � � t� t

2 t� �Adv.� t � �H�KH�H� t� t�

��

�z �KZ

�� t� t

�z �. �75�

The value of � at t � �t is obtained by solving thefollowing elliptic equation:

2 t�

�z �KZ

�� t� t

�z � � � t� t

� �2 t��Adv.� t � �H�KH�H� t� t�� t� t.

�76�

At the first implementation, the surface flux wastreated as a forcing term at the lower boundary condi-tion; however, such a treatment yielded computationalinstability when strong winds associated with a typhoonwere predicted around steep slopes. In the operationalversion of NHM, the surface flux at t � �t is computedfully implicitly using bulk coefficients.

Figure 9 shows the time sequences of surface (1.5 m)temperatures and dewpoint temperatures at Kuma-gaya, a city near Tokyo, on 5 June 2003 predicted byNHM. In this case, the maximum temperature reachedabout 30°C, but the maximum temperature by the pre-vious version of NHM was about 26°C. The observeddewpoint temperature was less than 15°C throughoutsimulation period, but the simulated dewpoint tem-perature increased in the daytime and exceeded 20°C.Obviously, these discrepancies were caused by the coldand wet biases in NHM. As shown in this figure, thesebiases are removed in the new NHM with the modifiedschemes (see sections 4d, 4e, 4f, and 4g).

h. Atmospheric radiation

Atmospheric radiation is based on Sugi et al. (1990),which was implemented to MRI/NPD-NHM as de-scribed in chapter G-5 of Saito et al. (2001a). The trans-fer function in longwave radiation is computed by arandom model of Goody (1952) in which absorption bywater vapor and carbon dioxide is considered. Short-wave radiation is computed by a two-stream approxi-mation method parameterized for wavelengths smallerthan 0.9 �m and larger than 0.9 �m. Absorbers consid-ered in the model are water vapor and cloud droplets.The band parameters are given by Lacis and Hansen(1974). Cloud fraction is parameterized using a pre-scribed function of relative humidity where the cloud isclassified into three categories as in Smagorinsky (1960)and critical values of humidity to compute cloud frac-tion are determined with reference to statistics by Ohnoand Isa (1984).

In the operational version of NHM, the upper limit todiagnose upper-level clouds has been changed from 300hPa of MRI/NPD-NHM to 100 hPa or tropopause

FIG. 9. Time sequences of the temperature and dewpoint tem-perature at 1.5-m height at Kumagaya, a city near Tokyo. Initialtime is 1800 UTC 4 Jun 2003. After Kumagai and Saito (2004).


level, to avoid an unnatural selective cooling near the300-hPa level. Optical depth for shortwave radiation ofupper-level clouds has been parameterized for pressurelevel to consider radiative properties of upper-levelclouds. The lower limit to diagnose lower-level cloudshas also been modified from 230 m of MRI/NPD-NHMto 500 m to ameliorate an unnatural cooling of the low-est level in the atmosphere over the ocean in winter.Computation of the radiation process is made every 15min with a spatially thinned-out operation by 20 kmhorizontally. This thinning is different from that ofMSM, where the radiation process is computed every60 min without a thinning in space, but gives almost nodifferences in the forecast result.

5. Verification and operational application

a. Verification of model performance: Winter 2004

To evaluate the performance of NHM as a mesoscaleNWP model, tests and verifications were carried out

with the same condition as in the operational run de-scribed in section 2. In advance of commencement ofthe preoperational daily runs of NHM, two test periods,summer 2003 and winter 2004, were selected to evalu-ate the quantitative performance of NHM. The periodsare 1) 16 days from 17 to 24 June 2003 and from 18 to25 July 2003 for summer, and 2) 16 days from 12 to 27January 2004 for winter. Sixty-four runs of 18-h fore-casts were conducted in each period. Since verificationof a preoperational test from April to August 2004 isdescribed in the next subsection, and its verificationresults are basically the same as in summer 2003, weshow only results of winter 2004 in this subsection.

Figures 10a and 10b show bias and threat scores for3-h-accumulated precipitation by MSM and NHM, re-spectively. In these figures, total scores for all 3-hourlyforecast times (FT � 3, 6, 9, 12, 15, and 18) in the testperiod from 12 to 27 January 2004 are calculated; thus384 cases are used to compute the total scores. Theverification grid size is 20 km, and verification is done

FIG. 10. (a) Bias scores for 3-h rain by MSM and NHM against threshold of rain intensity. Verification grid sizeis 20 km. Total scores for all forecast times (64 � 6 � 384 cases) for 16 days from 12 to 27 Jan 2004. (b) Same asin (a) but for threat score. (c) Time sequences of bias score for 5 mm (3 h)�1 by MSM and NHM. Total scores of64 cases for 16 days from 12 to 27 Jan 2004. (d) Same as in (c) but threat score.


using the JMA’s Radar-Automated MeteorologicalData Acquisition System (AMeDAS) analyzed precipi-tation for grid points over land and over sea within 40km from the coast. Apparently, bias scores of MSM aretoo large and exceed 5 for threshold values larger than10 mm (3 h)�1 (Fig. 10a). Bias scores of NHM alsoexceed unity for all threshold values; however, they re-main less than 3. It is well known that snow is oftenunderestimated in the Radar-AMeDAS analyzed pre-cipitation. This tendency may lead to these high biasscores of NWP models; however, in the case of MSM,simplification of precipitation processes such as the ne-glect of advection of snow is likely to cause overesti-mation of the orographic precipitation as mentionedlater. Threat scores of NHM prevail over those of MSMfor all threshold values except 15 mm (3 h)�1 (Fig. 10b).

Figures 10c and 10d show the time sequences of biasand threat scores by MSM and NHM for moderate pre-cipitation [5 mm (3 h)�1], respectively. Bias scores ofNHM increase with time and reach 2.5 at FT � 18, butthey are still obviously closer to unity than MSM.Threat scores of NHM prevail over those of MSM forall forecast times except FT � 9.

Figure 11 shows the histogram of 1-h precipitationintensity for model grids of MSM and NHM. Comparedwith the Radar-AMeDAS analysis, frequencies byMSM are too large for moderate to intense precipita-tion. The frequencies by NHM are also larger than theobservational values in most intensity, but relativelycloser to observation than MSM, which shows the sametendencies as bias scores shown in Fig. 10a.

Figure 12 shows the 3-h accumulated precipitationover central Japan at 0000 UTC 13 January 2004. In thiscase, a typical winter monsoon cold-air outbreak bringssnowfall over the mountainous region (for topography,see Fig. 1) of central Japan. Observed accumulated pre-cipitation is shown in Fig. 12a. In the correspondingforecast of MSM (Fig. 12b), intensity of precipitation isoverestimated and the location of precipitation is re-stricted to the windward side of the mountain ranges.These shortcomings of MSM are due to the moist pro-cess, wherein condensed water vapor over windwardmountain slope instantaneously turns to the surfaceprecipitation. In NHM (Fig. 12c), above overestimationof orographic snow is ameliorated, because evaporationand drift effects of cloud ice and snow are considered inthe prognostic cloud microphysical processes. Saito etal. (1996) conducted a numerical simulation of oro-graphic snowfall over the mountainous region of north-ern Japan and pointed out that snow drifts leewardmore than 20 km by the relatively small fall speed(about 1 m s�1). Similar results of improvement of oro-graphic precipitation (the luv-lee problem) by imple-mentation of the prognostic scheme have been reportedby Baldauf (2004) for the Lokal-Modell (LM) of Ger-many.

Figure 13 shows vertical cross sections of cloud wa-ter, cloud ice, graupel, and snow along the line A–B inFig. 12c. As shown in Fig. 13a, relatively flat cloud wa-ter area is seen over the Sea of Japan, whose cloud-topheight is about 2 km. Since the 0°C level is located nearsea surface in this case, this cloud area consists of su-

FIG. 11. Histogram of 1-h precipitation intensity for model grid by MSM and NHM. Hori-zontal axis is rain intensity, and vertical axis is frequency. Total for all forecast times for 16days from 12 to 27 Jan 2004.


percooled cloud water. At the windward slope of themountain range, the clouds increase their top heightsby the forced orographic updraft and turn to cloud ice,graupel, and snow. Most of the cloud water is confinedto the windward side, but cloud ice spreads aloft overthe mountain range and extends leeward (Fig. 13b).Graupel is confined at the windward side of mountain-top (Fig. 13c). On the other hand, snow falls from belowthe windward cloud area and about 4 km above themountain range and is drifted into the lee side of themountain range (Fig. 13d). Since fall velocity of snow isabout 1 m s�1, snow drifts 40 km leeward if snow fallsfrom 2.5 km above the ground level and the mean hori-zontal wind in the lower atmosphere is 15 m s�1.

To see the model performance to predict other me-teorological field, basic indexes such as the MSL pres-sure, 500-hPa height, and wind at 250 hPa were alsoverified (figure not shown), and almost neutral orslightly better scores were obtained against analysis andsonde.

b. Preoperational test: Summer 2004

After the verification of model performance for sum-mer 2003 and winter 2004, JMA started preoperationalruns of NHM on 29 March 2004 for final assessment(Saito et al. 2004). Preoperational runs were conductedon a 6-hourly time scale for 5 months until 31 August2004 and the forecast results were provided daily to theforecasters at local meteorological branches of JMA. Inthis subsection, verification results of NHM in the pre-operational period are presented to demonstrate itsperformance for summer.

Figures 14a and 14b show bias and threat scores for3-h precipitation, respectively. In this figure, totalscores for all 3-hourly forecast times (FT � 3, 6, 9, 12,15, and 18) are calculated; thus 3672 cases are used tocompute the scores. The bias scores of MSM are about1.2 for weak rain and slightly increase with the thresh-old values of rain intensity. In contrast, bias scores ofNHM gradually decrease with the threshold values ofrain intensity but are closer to 1.0 than MSM. Threatscores of NHM are almost equivalent to MSM for weakrain less than 5 mm (3 h)�1 while they prevail overMSM for moderate to intense rain greater than 10 mm(3 h)�1.

Figures 14c and 14d show the time sequences of biasand threat scores by MSM and NHM for moderate pre-cipitation [10 mm (3 h)�1], respectively. Bias scores ofNHM slightly increase with time and reach 1.2 at FT �18, but they are smaller than MSM. Threat scores ofNHM prevail over those of MSM for all forecast timesfrom FT � 3 to FT � 18. The advantage of NHM to

FIG. 12. (a) Observed 3-h accumulated precipitation over cen-tral Japan from 2100 UTC 12 Jan to 0000 UTC 13 Jan 2004. (b)Simulated 3-h precipitation over central Japan at 0000 UTC 13Jan 2004 by MSM. Initial time is 0600 UTC 12 Jan 2004. (c) Sameas in (b) but NHM.


MSM is clearer for more intense rain. Figures 14e and14f show the time sequences of bias and threat scoresfor 30 mm (3 h)�1, respectively. Bias scores of MSMincrease with time and reach 1.5 at FT � 18, but thoseof NHM are almost constant around 1.0. Threat scoresof NHM clearly prevail over those of MSM for all fore-cast times up to FT � 18. After FT � 6, all threat scoresof NHM are greater than MSM at FT � 6.

Figures 15 and 16 show the verification of forecastfields by MSM and NHM against sonde. MSM has anegative bias in prediction of height field in the loweratmosphere, but this tendency is ameliorated in NHM(Fig. 15a). The rmse of NHM is almost equivalent tothat of MSM above 500 hPa while it is smaller below700 hPa (Fig. 16a). As for the temperature field, NHMhas slight warming biases at 700–975-hPa levels (Fig.15b), while the rmse of NHM is almost equivalent toMSM at 700–975-hPa levels and is smaller than that ofMSM at 1000 hPa and above 500-hPa levels (Fig. 16b).

Biases of horizontal winds (Figs. 15c,d) show the sametendency in both models, while the rmse of NHM issmaller than that of MSM above 500-hPa levels (Figs.16c,d) as in the verification against analysis. Biases ofrelative humidity of NHM are smaller than MSM inmost levels (Fig. 15e), and the rmse of NHM is almostequivalent to MSM below 850-hPa levels and is smallerabove 700-hPa levels (Fig. 16e). The large biases andrmse of MSM above the 300-hPa level may be causedby the neglect of the ice phase in the MSM’s moistphysical processes.

In general, we conclude that NHM outperformsMSM in prediction of the meteorological fields.

c. Operational run

After the 5-month trial, the formal operation ofNHM started at JMA on 1 September 2004. It has beenrun on a 6-hourly time scale to provide 18-h short-range

FIG. 13. Vertical cross section of NHM forecast at FT � 18 (0000 UTC 13 Jan 2004) along line A–B in Fig. 12:(a) cloud water, (b) cloud ice, (c) graupel, (d) snow. Wind barbs indicate horizontal wind as the usual manner,where pennants show 50 kt.


forecast over Japan and its surrounding area. Here, weshow the NHM forecast whose initial time is 1200 UTC19 October as an example.

In 20 October, a strong typhoon hit western Japan.This typhoon, T0423 (TOKAGE), was initially orga-nized on 13 October over the sea around the MarianaIslands and moved northwestward. After the recurva-ture south of Okinawa Island on 18 October, it moved

northeastward and reached Shikoku on 20 October. InShikoku, a heavy rainfall exceeding 500 mm in totalprecipitation was observed. About 100 lives wereclaimed and more than 400 people were injured, whichwas the largest damage caused by a single typhoon inJapan after 1993.

Figure 17 shows the 9-hourly satellite infrared imagesobserved by Geostationary Operational Environmental

FIG. 14. (a), (b) Same as in Figs. 10a,b but total scores of all forecast times in 153 days (612 � 6 � 3672 cases)from 1 Apr to 31 Aug 2004. (c), (d) Same as in Figs. 10c,d but for 10 mm (3 h)�1. Total scores of 153 days (612cases) from 1 Apr to 31 Aug 2004. (e), (f) Same as in (c), (d) but for 30 mm (3 h)�1.


Satellite-9 (GOES-9) and corresponding MSL pressureby the Meso 4DVAR analysis from 1200 UTC 19 Oc-tober to 0600 UTC 20 October 2004. At 1200 UTC 19October, the typhoon TOKAGE was located aroundOkinawa Island (Fig. 17b). The cold dense overcast(CDO) around its center and associated spiral rainbands are evident (Fig. 17a). The typhoon movednortheastward and reached south of Kyushu at 2100UTC (Fig. 17d). The cloud-top height of CDO de-creased in the rear-side semicircle, suggesting intrusion

of dry air. Over the East China Sea, north–south-oriented low-level cloud streaks appear, suggesting theoutbreak of northerly cold air. At 0600 UTC 20 Octo-ber, TOKAGE reached Shikoku (Fig. 17f). The upperclouds vanished in the rear side (Fig. 17e). Figure 18shows the observed Radar-AMeDAS analyzed 3-h ac-cumulated precipitation. At 1200 UTC 19 October (Fig.18a), an area of precipitation by the typhoon is seenaround Okinawa Island. Another major rainfall areacorresponding to the midlatitude baroclinic frontal

FIG. 15. Mean error of forecasted fields by MSM andNHM at FT � 18 against sonde. Five-month statisticsfrom 1 Apr to 31 Aug 2004. (a) Height field (Z ). (b)Temperature (T ). (c) Horizontal wind (u). (d) Hori-zontal wind (v). (e) Relative humidity (RH).


zone widely covers the southern part of Japan, includ-ing its main island (Honshu), Kyushu, and Shikoku. At2100 UTC (Fig. 18b), the precipitation area of TOKAGEapproaches Kyushu, and intense orographic precipita-tion is seen in the southeastern part of Kyushu. An-other intense precipitation area is seen in the coastalarea of the southeastern part of the main island. At0600 UTC 20 October (Fig. 18c), the precipitation areaof TOKAGE was merged into the major rainfall area.(Enlarged views of the observed precipitation from

2100 UTC 19 October to 1200 UTC 20 October areshown in Fig. 20 and discussed later.)

Figure 19 shows the forecasted cloud and the MSLpressure by NHM corresponding to Fig. 17. In this fig-ure, the “forecasted satellite image” (Owada 2002) wasused to produce cloud images from NHM forecast,where the longwave radiation around 11 �m is com-puted from the predicted cloud fraction and water va-por by solving a radiative transfer equation. At the ini-tial time of NHM (1200 UTC 19 October), the cloud

FIG. 16. Same as in Fig. 15 but for rmse.


image (Fig. 19a) is produced by the initial condition ofthe water substances, which is given by the 6-h forecastof NHM whose initial time is 0600 UTC 19 October.Cloud water and cloud ice are removed at the gridpoints whose relative humidity of the Meso 4DVARanalysis is less than 90%. To initiate the typhoon struc-ture, typhoon bogus data using pseudo-observations(Koizumi 2003) at 0900 UTC are employed in the Meso4DVAR analysis.

At FT � 9, both the predicted cloud image and theMSL pressure (Figs. 19c and 19d) well reproduce thecharacteristics of the satellite observation and theanalysis (Figs. 17c and 17d). The low-level clouds pro-duced by a cold-air outbreak also appear over the EastChina Sea in the forecasted images. The major precipi-tation areas as well as the intense rain near Tokyoshown in Fig. 18b are also well predicted. At FT � 18(0600 UTC 20 October), the predicted typhoon reached

FIG. 17. (a) GOES-9 observed infrared image at 1200 UTC 19 Oct 2004. (b) MSL pressure by analysis at 1200 UTC19 Oct 2004. (c), (d) Same as in (a), (b) but at 2100 UTC. (e), (f) Same as in (a), (b) but at 0600 UTC 20 Oct.


south of Shikoku (Fig. 19f). Although the forecastedcloud image (Fig. 19e) well reproduces the major char-acteristics of Fig. 17e, upper clouds are excessively pre-sented over the Pacific Ocean south of 30°N. One of thepossible causes of this overestimation of upper clouds isomission of fallout of cloud ice in the cloud microphys-ics of NHM. On the hand, NHM simulated the move-ment and changes of TOKAGE and its associated rain-fall very well.

Figure 20 shows an enlarged view of the observed 3-haccumulated rain from 2100 UTC 19 October to 1200UTC 20 October by the Radar-AMeDAS analysis. At0300 UTC 20 October (Fig. 20c), very intense rainsexceeding 100 mm (3 h)�1 were observed at southeast-ern slopes of the mountainous areas in Shikoku. Theseintense rainfall areas move northeastward correspond-ing to the movement of the typhoon and reached thearea around Osaka at 1200 UTC (Fig. 20e).

Figure 21 shows the corresponding 3-h accumulatedrain from FT � 3 (2100 UTC 19 October) to FT � 18(1200 UTC 20 October) simulated by NHM initializedat 1800 UTC 19 October. The rainfall areas are gener-ally well simulated both in locations and intensities.Figure 22 shows the 3-h accumulated rain from 0300 to1200 UTC 20 October simulated by NHM, whose initialtime is 0000 UTC 19 October. Compared with the cor-responding observation (Figs. 20c–f), the intense rain-fall areas are excellently simulated. These figures (Figs.2a–d) are also very similar to the predictions of NHM atthe same valid times initiated from 1800 UTC 19 Oc-tober (Figs. 21c–f). These similarities show the consis-tencies of the prediction and demonstrate the reliabilityof the forecasts of NHM.

6. Summary and concluding remarks

An operational nonhydrostatic mesoscale model hasbeen developed at JMA based on the MRI/NPD uni-fied nonhydrostatic model. Several points have beenrevised for operational NWP with a horizontal resolu-tion of 10 km. Two map factors are incorporated andthe buoyancy term is evaluated from density perturba-tion. A time-splitting scheme for advection and gravitywaves is developed to enhance model robustness,where a low-order (second order) part of advection ismodified in the latter half of the leapfrog time integra-tion. Diffusion of water vapor is considered in additionto the fallout of precipitation in the continuity equa-tion, where the density is defined by the sum of moistair and water substances. In the physical processes, theKain–Fritsch scheme is implemented, wherein severalrevisions are made to improve its performance to pre-dict heavy rainfall events in Japan. The targeted mois-

FIG. 18. (a) Observed Radar-AMeDAS precipitation from 0900to 1200 UTC 19 Oct 2004. (b) Same as in (a) but from 1800 to 2100UTC 19 Oct 2004. (c) Same as in (a) but from 0300 to 0600 UTC20 Oct 2004.


ture diffusion is implemented to attenuate the gridpointstorms. A new PBL scheme that considers nonlocaleffect is implemented with a new TKE diagnosticscheme.

In the test runs, verifications show that NHM hasneutral or slightly better performance than MSM topredict meteorological fields in both winter and sum-

mer. Better performance is found in the precipitationforecast. Obviously, drift of condensed water sub-stances is simulated better in NHM, which yields im-provement of orographic precipitation especially inwinter. In the 5-month preoperational period, clear ad-vantages of NHM to predict meteorological fields andprecipitation were shown. On 1 September 2004 JMA

FIG. 19. (a) Forecasted cloud by NHM at 1200 UTC 19 Oct 2004. (b) MSL pressure of NHM at initial time(1200 UTC 19 Oct 2004). (c), (d) Same as in (a), (b) but at FT � 9. (e), (f) Same as in (a), (b) but at FT � 18.


formally replaced its operational hydrostatic mesoscalemodel with NHM, as the nonhydrostatic mesoscalemodel (MSM). NHM is now used at the Hong KongObservatory as well for the operation of the Rainstorm

Analysis and Prediction Integrated Data-processingSystem (RAPIDS; Li et al. 2005)

Although the horizontal resolution 10 km is the sameas in the hydrostatic MSM at the first operation of

FIG. 20. Observed Radar-AMeDAS 3-h precipitation: (a) 2100 UTC 19 Oct, (b) 0000, (c) 0300, (d) 0600, (e)0900, and (f) 1200 UTC 20 Oct 2004.


NHM, after the replacement of the supercomputer sys-tem of JMA scheduled in March 2006, the horizontalresolution of NHM will be enhanced to 5 km. Themodel will be operated on a 3-hourly time scale, 8 times

a day. Forecast time will be extended to 33 h in March2007, when a high-resolution (20 km) semi-Lagrangianglobal model becomes operational and supplies bound-ary condition to NHM 6 hourly. A nonhydrostatic

FIG. 21. Forecasted 3-h precipitation by NHM with the initial time of 1800 UTC 19 Oct 2004: (a) FT � 3, (b)FT � 6, (c) FT � 9, (d) FT � 12, (e) FT � 15, and (f) FT � 18.


4DVAR data assimilation system [JMA nonhydrostaticmodel-based variational data assimilation system(JNoVA)] is under development and will become op-erational in late 2007 to supply NHM with the initialconditions. A higher-resolution version of NHM hasbeen tested in MRI and NPD to realize a dynamicalshort-range forecast with a cloud-resolving model in thefuture.

Acknowledgments. Many people from NPD/JMAand MRI contributed to the development of NHM andrecent operational implementation. The authors aregrateful to Tomonori Hara, Masami Narita, EijiToyoda, Tabito Hara, Hiroshi Nakayama, Yuki Honda,and Susumu Goto of NPD, and Fumiaki Fujibe, Aki-hiko Murata, Wataru Mashiko, and Shugo Hayashi ofMRI for their contribution and assistance to developand verify this model. We also thank Nobuo Sato andTadashi Tsuyuki of NPD and Masanori Yoshizaki of

MRI for their continuous encouragement and valuablecomments. A part of the source codes of the Kain–Fritsch scheme in this nonhydrostatic model was devel-oped with reference to the program of the WeatherResearch and Forecast Model of NCAR by the specialcourtesy of Dr. Jack Kain of NSSL and Dr. Jimy Du-dhia of NCAR. Thanks are extended to ProfessorToshiki Iwasaki of Tohoku University; Professor Hi-roshi Niino and Dr. Masaru Yoshida of the Ocean Re-search Institute, University of Tokyo; Professors Aki-masa Sumi and Masahide Kimoto of CCSR, Universityof Tokyo; and Professor Mikio Nakanishi of the Na-tional Defense Academy in Japan for their cooperationand suggestions. We express our deepest respect to theachievements of the late Dr. Motohki Ikawa, whopassed away in 1991. We also express our heartfelt re-gret for the untimely passing away in October 2003 ofthe late Dr. Hajime Nakamura, former director ofNPD, who gave us tremendous support to develop an

FIG. 22. Forecasted 3-h precipitation by NHM with the initial time of 0000 UTC 20 Oct 2004: (a) FT � 3, (b)FT � 6, (c) FT � 9, (d) FT � 12.


operational mesoscale nonhydrostatic NWP model atJMA.

Finally, the authors wish to thank two anonymousreviewers for their comments, which led to substantialimprovements in the presentation of the material.

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The Operational JMA Nonhydrostatic Mesoscale Model · The model is based on the MRI/NPD unified...

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