**The JMA Nonhydrostatic Model and Its Applications to Operation and Research**

Kazuo Saito

*Meteorological Research Institute Japan* 

#### **1. Introduction**

84 Atmospheric Model Applications

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Nonhydrostatic models were initially developed as research tools for small scale meteorological phenomena. Today, several nonhydrostatic models have been developed and applied to numerical simulations and operational numerical weather prediction (NWP). In this chapter, we review the Japan Meteorological Agency (JMA) nonhydrostatic model (JMA-NHM, hereafter referred to as NHM) and its applications to operational forecasts and research fields. Section 2 presents a brief history of the model development from a research tool to a full-scale NWP model. In section 3, we review applications of the model to several research fields of various time/spatial scales from tornado to regional climate modelling, and mesoscale data assimilation and ensemble prediction studies. Section 4 introduces ongoing relevant topics including the Japanese next generation supercomputer project.

#### **2. The JMA nonhydrostatic model**

#### **2.1 Development of NHM at MRI**

The JMA nonhydrostatic model (NHM) was first developed as a research tool at the Meteorological Research Institute (MRI). Ikawa (1988) developed a nonhydrostatic model with orography and compared computational schemes with a 2-dimensional numerical experiment. Following Gal-Chen and Somerville (1975), the terrain-following vertical coordinates

$$z^\* = \frac{H(z - z\_s)}{H - z\_s},\tag{1}$$

and the metric tensors for the coordinate transformations were employed:

$$\mathbf{G}^{\frac{1}{2}} = \mathbf{1} - \frac{\underline{\mathbf{z}\_s}}{\underline{H}}, \qquad \mathbf{G}^{\frac{1}{2}} \mathbf{G}^{13} = (\frac{\mathbf{\stackrel{\ast}{Z}}}{\underline{H}} - \mathbf{1}) \frac{\mathbf{\stackrel{\ast}{\mathcal{O}z\_s}}}{\boldsymbol{\varepsilon}\mathbf{x}}, \qquad \mathbf{G}^{\frac{1}{2}} \mathbf{G}^{23} = (\frac{\mathbf{\stackrel{\ast}{\mathcal{Z}}}}{\underline{H}} - \mathbf{1}) \frac{\mathbf{\stackrel{\ast}{\mathcal{O}z\_s}}}{\boldsymbol{\varepsilon}\mathbf{y}}, \tag{2}$$

where *zs* is the surface height and *H* is the model top height.

#### **2.1.1 Anelastic equation model**

The first version of NHM used the anelastic (AE) scheme to solve the Navier-Stokes momentum equations for a fluid. The AE model removes sound waves from solutions in the

The JMA Nonhydrostatic Model and Its Applications to Operation and Research 87

where subscripts *c, r, i, s* and *g* stand for the cloud water, rain, cloud ice, snow, and graupel,

<sup>2</sup> *G DIVT PRC*, *<sup>t</sup>*

() , *UV W DIVT m <sup>m</sup>*

<sup>1</sup> *W W mG G U G G V* \*{ ( )}.

\* ( ), *PRC Va rr a ss a g g q V q V q*

water substances (rain, snow and graupel, respectively). The state equation is given as the

0 / 0 () , *C C v p*

In the AE model, the buoyancy term was computed from the perturbations of potential temperature and pressure, but in the fully compressible model, it is directly computed from

*<sup>m</sup>* ( ), *<sup>P</sup> C PFT DIVT PRC*

where *Cm* is the sound wave speed and *PFT* is the local time tendency of the mass-virtual

*m p p R p*

*<sup>a</sup>* is the density of moist air, and *Vr,Vs and Vg* the terminal velocity of precipitable

1 1 1 2 2 2 ,, , *G u Gv Gw UV W mm m*

\* 2

*xy z*

1 1 13 23 2 2

*<sup>v</sup>* that of water vapor.

\*

 (10)

(11)

(12)

(13)

*q qqqqq* (14)

(15)

(9)

 

> 

 

*d* is the density of dry air and

Introducing a map factor *m*, the continuity equation is given by

> 1 2

*G*

*PRC* in (8) is the fall-out of water substances written in *z\** coordinate:

*z* 

> > 2

*<sup>m</sup>* is the mass-virtual potential temperature defined by

(1 0.608 )(1 *<sup>m</sup>* ). *v cris <sup>g</sup>*

*t* 

 

The pressure equation is obtained from (8) and (13) as

1

where *DIVT* is the total divergence in z\* coordinate and *U*, *V*, and *W\** are defined by

respectively.

where 

where 

diagnostic equation for density:

the density perturbation.

potential temperature.

,

*dvcrisg* (7)

(8)

equation system by scale analysis (Ogura and Phillips, 1962). Field variables are divided into the time independent horizontal uniform reference state  *(z)* and its perturbation *' (x, y, z, t)*  as

$$p = \overline{p} + p^{\prime}, \qquad \rho = \overline{\rho} + \rho^{\prime}, \quad \theta = \overline{\theta} + \theta^{\prime} \quad . \tag{3}$$

Following Clark (1977), the continuity equation was given by

$$
\hat{D}IVT = \frac{\partial \mathcal{U}}{\partial \mathbf{x}} + \frac{\partial \mathcal{V}}{\partial y} + \frac{\partial \mathcal{W}}{\partial \mathbf{z}}^\* = \mathbf{0},
\tag{4}
$$

where *U*, *V*, and *W* are momentum multiplied by the metric tensor as the prognostic variables in the model:

$$\mathcal{U} = \overline{\rho} \mathcal{G}^{\frac{1}{2}} u, \quad V = \overline{\rho} \mathcal{G}^{\frac{1}{2}} v, \quad \mathcal{W} = \overline{\rho} \mathcal{G}^{\frac{1}{2}} w,\tag{5}$$

$$\mathcal{W}^\* = \frac{1}{\frac{1}{G^2}} \{\mathcal{W} + \mathcal{G}^2 \mathcal{G}^{13} \mathcal{U} + \mathcal{G}^{\frac{1}{2}} \mathcal{G}^{23} \mathcal{V}\} \,. \tag{6}$$

Taking the total divergence of the momentum equation yields a 3-dimensional Poisson-type pressure diagnostic equation, which was solved by the Dimension Reduction Method.

This model was further evolved by including a bulk cloud microphysics scheme based on Lin et al. (1983), a turbulent closure model based on Deardorff (1980), and treatment surface processes for sea and land. Comprehensive documentation was published in the Technical Report of MRI (Ikawa and Saito, 1991) as a nonhydrostatic model developed at the Forecast Research Department of MRI.

#### **2.1.2 Nested model**

Ikawa and Saito's (1991) model was modified to a nested model (MRI-NHM) to realistically simulate mesoscale phenomena (Saito, 1994). For the dynamical core, the AE scheme was adopted. Variational calculus (Sherman, 1978) was implemented to obtain a non-divergent mass consistent initial field, where the continuity equation (4) was used as the strong constraint to modify the interpolated wind field. Orlanski's (1976) radiation condition was employed with the time-dependent lateral boundary condition, and mass fluxes through the lateral boundaries were adjusted to maintain mass conservation.

A hydrostatic version of MRI-NHM was developed by Kato and Saito (1995) and was used to examine the applicability of hydrostatic approximation to a high-resolution simulation of moist convection.

#### **2.1.3 Fully compressible version with a map factor**

Saito (1997) developed a semi-implicit, fully compressible version of MRI-NHM including a map factor, where linearization using the reference atmosphere was removed. Density was defined by the sum of masses of moist air and the water substances per unit volume as

$$\rho \equiv \rho\_d + \rho\_v + \rho\_c + \rho\_r + \rho\_i + \rho\_s + \rho\_s \tag{7}$$

where subscripts *c, r, i, s* and *g* stand for the cloud water, rain, cloud ice, snow, and graupel, respectively. *d* is the density of dry air and *<sup>v</sup>* that of water vapor.

Introducing a map factor *m*, the continuity equation is given by

86 Atmospheric Model Applications

equation system by scale analysis (Ogura and Phillips, 1962). Field variables are divided into

*ppp* ', 

> \* 0, *UVW DIVT x y z*

where *U*, *V*, and *W* are momentum multiplied by the metric tensor as the prognostic

<sup>1</sup> *W W GG U GG V* \* ( ) .

Taking the total divergence of the momentum equation yields a 3-dimensional Poisson-type pressure diagnostic equation, which was solved by the Dimension Reduction Method.

This model was further evolved by including a bulk cloud microphysics scheme based on Lin et al. (1983), a turbulent closure model based on Deardorff (1980), and treatment surface processes for sea and land. Comprehensive documentation was published in the Technical Report of MRI (Ikawa and Saito, 1991) as a nonhydrostatic model developed at the Forecast

Ikawa and Saito's (1991) model was modified to a nested model (MRI-NHM) to realistically simulate mesoscale phenomena (Saito, 1994). For the dynamical core, the AE scheme was adopted. Variational calculus (Sherman, 1978) was implemented to obtain a non-divergent mass consistent initial field, where the continuity equation (4) was used as the strong constraint to modify the interpolated wind field. Orlanski's (1976) radiation condition was employed with the time-dependent lateral boundary condition, and mass fluxes through the

A hydrostatic version of MRI-NHM was developed by Kato and Saito (1995) and was used to examine the applicability of hydrostatic approximation to a high-resolution simulation of

Saito (1997) developed a semi-implicit, fully compressible version of MRI-NHM including a map factor, where linearization using the reference atmosphere was removed. Density was defined by the sum of masses of moist air and the water substances per unit volume as

1 2

*G*

lateral boundaries were adjusted to maintain mass conservation.

**2.1.3 Fully compressible version with a map factor** 

11 1 22 2 *U Gu V Gv W Gw*

> 1 1 13 23 2 2

 

\*

 

 *(z)* and its perturbation

(4)

,, , (5)

(6)

', ' . (3)

*' (x, y, z, t)* 

the time independent horizontal uniform reference state

Following Clark (1977), the continuity equation was given by

as

variables in the model:

Research Department of MRI.

**2.1.2 Nested model** 

moist convection.

$$\mathbf{G}^{\frac{1}{2}} \frac{\partial \rho}{\partial t} + \mathbf{D} \mathbf{I} \mathbf{V} \mathbf{T} = \mathbf{P} \mathbf{R} \mathbf{C} \tag{8}$$

where *DIVT* is the total divergence in z\* coordinate and *U*, *V*, and *W\** are defined by

$$
\hat{D}IVT = m^2(\frac{\partial \mathcal{U}}{\partial \mathbf{x}} + \frac{\partial V}{\partial \mathbf{y}}) + m\frac{\partial \mathcal{W}}{\partial \mathbf{z}^\*}\,'\,\tag{9}
$$

$$\mathcal{U} = \frac{\rho \mathcal{G}^2 u}{m}, \quad \mathcal{V} = \frac{\rho \mathcal{G}^2 v}{m}, \quad \mathcal{W} = \frac{\rho \mathcal{G}^2 w}{m}, \tag{10}$$

$$\mathcal{W}^\* = \frac{1}{\frac{1}{G^2}} \{ \mathcal{W} + m \langle \mathcal{G}^2 G^{13} \mathcal{U} + \mathcal{G}^2 G^{23} V \rangle \}. \tag{11}$$

*PRC* in (8) is the fall-out of water substances written in *z\** coordinate:

$$PRC = \frac{\partial}{\partial \ z^\*} (\rho\_a V\_r \eta\_r + \rho\_a V\_s \eta\_s + \rho\_a V\_g \eta\_g), \tag{12}$$

where *<sup>a</sup>* is the density of moist air, and *Vr,Vs and Vg* the terminal velocity of precipitable water substances (rain, snow and graupel, respectively). The state equation is given as the diagnostic equation for density:

$$\rho = \frac{p\_0}{R\theta\_m} (\frac{p}{p\_0})^{\mathbb{C}\_v/\mathbb{C}\_p} \, \, \, \, \, \tag{13}$$

where *<sup>m</sup>* is the mass-virtual potential temperature defined by

$$
\theta\_m = \theta (1 + 0.608 q\_v) (1 - q\_c - q\_r - q\_i - q\_s - q\_g) \,. \tag{14}
$$

In the AE model, the buoyancy term was computed from the perturbations of potential temperature and pressure, but in the fully compressible model, it is directly computed from the density perturbation.

The pressure equation is obtained from (8) and (13) as

$$\frac{\partial P}{\partial t} = \mathcal{C}\_m{}^2 \{PFT - DIVT + PRC\} \,\prime \tag{15}$$

where *Cm* is the sound wave speed and *PFT* is the local time tendency of the mass-virtual potential temperature.

The JMA Nonhydrostatic Model and Its Applications to Operation and Research 89

Several points in the K-F scheme were revised to improve its performance as a mesoscale NWP model in Japan, where a moist and unstable maritime air mass prevails in summer. The targeted moisture diffusion (TMD) was implemented to attenuate the grid-point storms and the associated intense grid-scale precipitation (Saito and Ishida, 2005), where an artificial second-order horizontal diffusion is applied to water vapor when strong upward

On 1 September 2004, JMA replaced the former hydrostatic mesoscale model (hydrostatic MSM) with NHM (a nonhydrostatic MSM). Eighteen-hour forecasts were run four times a day to support disaster prevention and the very short-range forecast of precipitation at JMA. A domain of 3600 km x 2880 km that covers Japan and its surrounding areas was taken. Vertically, 40 levels with variable grid intervals were employed, where the model top was

Initial conditions of horizontal wind, temperature, water vapor, and surface pressure were given by the JMA Meso 4D-Var (Koizumi et al., 2005) six-hourly analyses, as in the former hydrostatic MSM. Initial conditions of cloud microphysical quantities were given by the sixhourly forecast-forecast cycle. Details of the 10 km nonhydrostatic MSM are given in Saito et

In March 2006, horizontal and vertical resolutions of the nonhydrostatic MSM were enhanced from 10 km L40 to 5 km L50. The model operation was also increased from four times a day (six hourly) to eight times (three hourly), to provide more frequent forecasts. Several modifications were added to physical processes. In the atmospheric radiation scheme of the 10 km MSM, a cloud was assumed as a black body and cloud optical properties were given by empirical constants. In the new radiation scheme, cloud optical properties were determined by cloud water/ice contents and their effective radius, which reduced the negative bias of the upper air temperature. Convective parameterization was still required at 5 km, because without convective parameterization the model overestimated intense rain and underestimated weak to moderate rains. In the K-F scheme, the following revisions were made (Ohmori and Yamada 2006): (1) conversion from convective condensate to rain was reduced, (2) time scales of deep and shallow convection were reduced, and (3) threshold values for

In May 2007, JMA extended the forecast time of MSM from 15 to 33 hours at the initial times of 03, 09, 15 and 21 UTC to provide information for disaster prevention up to 24 hours (Hara

was introduced, which approaches the *z\** coordinate near the surface and the *z* coordinate

out of cloud ice was considered in addition to rain, snow, and graupel in order to prevent excessive accumulation of cloud ice in the upper model atmosphere. In the K-F scheme for

( ), *<sup>s</sup>*

(17)

*)* is determined so that *∂z/∂*

*)* is differentiable. In the cloud microphysics, fall-

et al., 2007). To modify the dynamics, the generalized hybrid vertical coordinate,

*z zf*

motions exist.

al. (2006).

**2.2.2 Operational MSM** 

located at 22 km and the lowest level was 20 m.

conversion from cloud water/ice to precipitation were increased.

near the model top (Ishida, 2007). Here, *f*(0) = 1, *f*(*H*) = 0, *and f(*

is positive and the second derivative of *f(*

**2.2.3 Upgrade of MSM after 2006** 

To stabilize the acoustic mode, the HI-VI (Horizontally Implicit-Vertically Implicit) scheme, which treats sound waves implicitly for both vertical and horizontal directions, was used. This scheme, often referred as the *semi-implicit* method, was first implemented by Tapp and White (1976). A 3-dimensional Helmholtz pressure equation, which is formally similar to the Poisson equation in the AE model, is obtained by HI-VI treatment of sound waves. For details, see Saito (1997) and Saito et al. (2007).

#### **2.1.4 MRI/NPD-NHM**

In 1999, a cooperative effort to develop a community model for NWP and research started between the Numerical Prediction Division (NPD) of JMA and MRI. The HE-VI (Horizontally Explicit-Vertically Implicit) scheme, which solves a vertically 1-dimensional Helmholtz-type pressure equation, was re-implemented into MRI-NHM by Muroi et al. (2000). Code parallelization of the model was also performed to cope with the distributed memory parallel computers. A flux limiter advection correction scheme (Kato, 1998) was implemented to reduce numerical errors due to the finite difference approximation and to assure monotonicity. In the cloud physics, the box Lagrangian scheme (Kato 1995) was introduced to assure computational stability for sedimentation of rain.

A comprehensive description of the unified model (MRI/NPD-NHM) was published in the Technical Report of MRI (Saito et al., 2001a).

#### **2.2 Operational applications**

#### **2.2.1 Development at NPD/JMA**

In 2001, full-scale development of an operational nonhydrostatic mesoscale model at JMA (NHM) was started at NPD in collaboration with MRI. Several modifications were added to enhance computational efficiency, robustness, and accuracy for an operational NWP model.

Higher-order (third to fifth) advection schemes that consider a staggered grid configuration were implemented by Fujita (2003). The fourth-order scheme was chosen for the operational forecasting, considering computational cost and matching with the advection correction scheme. A time-splitting scheme of gravity waves and advection terms was implemented by Saito (2003). In this scheme, higher-order advection terms with advection correction were fully evaluated at the center of the leapfrog time step; the lower-order (second-order) components at each short time step were then adjusted in the latter half of the leapfrog time integration. In the continuity equation, the diffusion of water vapor in unit time, which includes sub-grid scale turbulent mixing and computational diffusion, was considered by Saito (2004) as

$$
\mathcal{G}^{\frac{1}{2}} \frac{\partial \mathcal{p}}{\partial t} + \mathcal{D}IV\mathcal{T} = \mathcal{P}\mathcal{R}\mathcal{C} + \mathcal{\rho}\mathcal{D}IFq\_{\upsilon}.\tag{16}
$$

This term was implemented to consider the surface evaporation of water vapor, which offsets the loss of mass by precipitation in total mass conservation.

As for physical processes, the Kain-Fritsch convective parameterization scheme (K-F scheme; Kain and Fritsch, 1993) was implemented with modification by Yamada (2003). Several points in the K-F scheme were revised to improve its performance as a mesoscale NWP model in Japan, where a moist and unstable maritime air mass prevails in summer. The targeted moisture diffusion (TMD) was implemented to attenuate the grid-point storms and the associated intense grid-scale precipitation (Saito and Ishida, 2005), where an artificial second-order horizontal diffusion is applied to water vapor when strong upward motions exist.

#### **2.2.2 Operational MSM**

88 Atmospheric Model Applications

To stabilize the acoustic mode, the HI-VI (Horizontally Implicit-Vertically Implicit) scheme, which treats sound waves implicitly for both vertical and horizontal directions, was used. This scheme, often referred as the *semi-implicit* method, was first implemented by Tapp and White (1976). A 3-dimensional Helmholtz pressure equation, which is formally similar to the Poisson equation in the AE model, is obtained by HI-VI treatment of sound waves. For

In 1999, a cooperative effort to develop a community model for NWP and research started between the Numerical Prediction Division (NPD) of JMA and MRI. The HE-VI (Horizontally Explicit-Vertically Implicit) scheme, which solves a vertically 1-dimensional Helmholtz-type pressure equation, was re-implemented into MRI-NHM by Muroi et al. (2000). Code parallelization of the model was also performed to cope with the distributed memory parallel computers. A flux limiter advection correction scheme (Kato, 1998) was implemented to reduce numerical errors due to the finite difference approximation and to assure monotonicity. In the cloud physics, the box Lagrangian scheme (Kato 1995) was

A comprehensive description of the unified model (MRI/NPD-NHM) was published in the

In 2001, full-scale development of an operational nonhydrostatic mesoscale model at JMA (NHM) was started at NPD in collaboration with MRI. Several modifications were added to enhance computational efficiency, robustness, and accuracy for an operational NWP model. Higher-order (third to fifth) advection schemes that consider a staggered grid configuration were implemented by Fujita (2003). The fourth-order scheme was chosen for the operational forecasting, considering computational cost and matching with the advection correction scheme. A time-splitting scheme of gravity waves and advection terms was implemented by Saito (2003). In this scheme, higher-order advection terms with advection correction were fully evaluated at the center of the leapfrog time step; the lower-order (second-order) components at each short time step were then adjusted in the latter half of the leapfrog time integration. In the continuity equation, the diffusion of water vapor in unit time, which includes sub-grid scale turbulent mixing and computational diffusion, was considered by

<sup>2</sup> . *G DIVT PRC DIF <sup>v</sup> <sup>q</sup> <sup>t</sup>*

This term was implemented to consider the surface evaporation of water vapor, which

As for physical processes, the Kain-Fritsch convective parameterization scheme (K-F scheme; Kain and Fritsch, 1993) was implemented with modification by Yamada (2003).

(16)

introduced to assure computational stability for sedimentation of rain.

1

offsets the loss of mass by precipitation in total mass conservation.

details, see Saito (1997) and Saito et al. (2007).

Technical Report of MRI (Saito et al., 2001a).

**2.2 Operational applications 2.2.1 Development at NPD/JMA** 

Saito (2004) as

**2.1.4 MRI/NPD-NHM** 

On 1 September 2004, JMA replaced the former hydrostatic mesoscale model (hydrostatic MSM) with NHM (a nonhydrostatic MSM). Eighteen-hour forecasts were run four times a day to support disaster prevention and the very short-range forecast of precipitation at JMA. A domain of 3600 km x 2880 km that covers Japan and its surrounding areas was taken. Vertically, 40 levels with variable grid intervals were employed, where the model top was located at 22 km and the lowest level was 20 m.

Initial conditions of horizontal wind, temperature, water vapor, and surface pressure were given by the JMA Meso 4D-Var (Koizumi et al., 2005) six-hourly analyses, as in the former hydrostatic MSM. Initial conditions of cloud microphysical quantities were given by the sixhourly forecast-forecast cycle. Details of the 10 km nonhydrostatic MSM are given in Saito et al. (2006).

#### **2.2.3 Upgrade of MSM after 2006**

In March 2006, horizontal and vertical resolutions of the nonhydrostatic MSM were enhanced from 10 km L40 to 5 km L50. The model operation was also increased from four times a day (six hourly) to eight times (three hourly), to provide more frequent forecasts. Several modifications were added to physical processes. In the atmospheric radiation scheme of the 10 km MSM, a cloud was assumed as a black body and cloud optical properties were given by empirical constants. In the new radiation scheme, cloud optical properties were determined by cloud water/ice contents and their effective radius, which reduced the negative bias of the upper air temperature. Convective parameterization was still required at 5 km, because without convective parameterization the model overestimated intense rain and underestimated weak to moderate rains. In the K-F scheme, the following revisions were made (Ohmori and Yamada 2006): (1) conversion from convective condensate to rain was reduced, (2) time scales of deep and shallow convection were reduced, and (3) threshold values for conversion from cloud water/ice to precipitation were increased.

In May 2007, JMA extended the forecast time of MSM from 15 to 33 hours at the initial times of 03, 09, 15 and 21 UTC to provide information for disaster prevention up to 24 hours (Hara et al., 2007). To modify the dynamics, the generalized hybrid vertical coordinate,

$$
\zeta = z - z\_s f(\zeta) \tag{17}
$$

was introduced, which approaches the *z\** coordinate near the surface and the *z* coordinate near the model top (Ishida, 2007). Here, *f*(0) = 1, *f*(*H*) = 0, *and f()* is determined so that *∂z/∂* is positive and the second derivative of *f()* is differentiable. In the cloud microphysics, fallout of cloud ice was considered in addition to rain, snow, and graupel in order to prevent excessive accumulation of cloud ice in the upper model atmosphere. In the K-F scheme for

The JMA Nonhydrostatic Model and Its Applications to Operation and Research 91

Fig. 1. Threat score of MSM for three-hour precipitation averaged for FT = 3 to 15 with a threshold value of 5 mm/3 hour from March 2001 to November 2011. The red broken line denotes the monthly value, while the black solid line indicates the 12-month running mean.

Year. Month Modification 2001. 3 Start of Mesoscale NWP (10kmL40+OI)

2003. 10 SSM/I microwave radiometer data

2005. 3 Doppler radar radial winds data

2007. 5 Upgrade of physical processes 2009. 4 Nonhydrostatic 4D-Var

Table 1. Modifications for operational mesoscale NWP at JMA.

2006. 3 Enhancement of model resolution (5kmL50)

2009. 10 GPS total precipitable water vapor (TPWV) data 2011. 6 Water vapor data retirieved from radar reflectivity

2004. 7 QuikSCAT Seawinds data 2004. 9 Nonhydrostatic model

2001. 6 Wind profiler data 2002. 3 Meso 4D-Var

Courtesy of NPD/JMA.

convection, perturbation depending on relative humidity was added in the trigger function to reduce the overestimation of convective rain induced by orography. For the turbulent model, a Mellor and Yamada level-3 closure model (MYNN3; Nakanishi and Niino, 2004; 2006) was implemented first as the operational NWP model to reduce model bias in the boundary layer (Hara, 2007). In addition to the prognostic turbulent kinetic energy (*TKE*), fluctuations of liquid water potential temperature (*<sup>l</sup>*'2), total water content (*qw*'2), and their correlation (*<sup>l</sup>*'*qw*') were treated as prognostic variables. To evaluate the degree of cloudiness, partial condensation computed by the probability density function in MYNN3 was considered. Results of these modifications are given in Saito et al. (2007)

A nonhydrostatic 4D-Var data assimilation system (JNoVA; JMA Nonhydrostatic model based Variational data assimilation system) (Honda et al., 2005) was implemented in April 2009 to supply MSM more accurate initial conditions (Honda and Sawada, 2008). The horizontal resolution of the 4D-Var inner-loop model was enhanced from 20 km of Meso 4D-Var to 15 km in JNoVA.

### **2.2.4 QPF performance of MSM**

Figure 1 plots the quantitative precipitation forecast (QPF) performance of MSM since it began actual operation (March 2001) to November 2011. In this figure, threat scores averaged for FT=3 to 15 for moderate rain with a threshold value of 5 mm in 3 hours are indicated. The verification grid size is 20 km. The averaged score in 2001 was about 0.2, but the score improved year by year, and the latest score approaches 0.4. Given the fact that statistical PQF performance of high resolution regional models is sometimes notoriously bad due to the difficulty of predicting mesoscale precipitation and the *double penalty* problem, this threat score improvement is remarkable.

Table 1 lists the main modifications added to the operational mesoscale NWP at JMA from 2001 to 2011. In addition to the modifications discussed in the former subsections, the global positioning system (GPS)-derived total precipitable water vapor (TPWV) data (Ishikawa, 2010) has been assimilated since October 2009, and the 1D-Var retrieved water vapor data from radar reflectivity (Ikuta and Honda, 2011) has been used since June 2011. These modifications have contributed to the recent improvement of the QPF performance of MSM through improving water vapor analysis.

#### **2.2.5 Mesoscale tracer transport model**

The GPV of the operational MSM is used as input to the atmospheric transport model at MRI and JMA. This mesoscale ATM takes a Lagrangian scheme (Seino et al., 2004) with many tracer particles that follow advection, horizontal and vertical diffusion, fallout, and dry and wet deposition processes. JMA incorporated photochemical oxidant information in June 2007 (Takano et al., 2007) and the tephra fall forecast in March 2008 (Shimbori et al., 2010).
