Development of the MRI/NPD Nonhydrostatic Model

Chiashi Muroi*
Numerical Prediction Division
Japan Meteorological Agency

1. Introduction

The JMA has operated a mesoscale regional NWP model for preventing natural disaster since 1998. The horizontal resolution of the model is 10km. It is, however, still at a trial stage. We have a plan to replace our supercomputer in 2001 and upgrade the mesoscale NWP system. Primitive equations and a spectral method are applied to the current operational regional model. A nonhydrostatic model is, however, recommended for a higher resolution NWP system in the near future. The Meteorological Research Institute of JMA has developed nonhydrostatic model, MRI-NHM(Saito and Kato, 1997), and many numerical studies have been conducted using the MRI-NHM. On the other hand, the Numerical Prediction Division of JMA has been also involved in development of numerical weather prediction models. We, MRI and NPD, have agreed that we combine both efforts and shall develop a unified nonhydrostatic model, "MRI/NPD-NHM", for both operational and research communities together since 1999.

2. Specification of the MRI/NPD nonhydrostatic model

Wider spread of parallel supercomputers and requirement of community mesoscale models give us a motivation to enhance portability of the source code of the model. We introduce a split-explicit time integration scheme (HE-VI) in MRI/NPD-NHM, while a semi-implicit scheme (HI-VI) is incorporated to the original MRI-NHM. This split-explicit scheme is efficient on parallel machines because it requires little communication between distributed memories while the semi-implicit scheme needs all-to-all communication. Since the governing equation is compressible, sound mode are also included by the model. This situation severely restrict the time step of time integration scheme. To avoid this restriction, the split technique is employed.

Horizontal Momentum Equations

\begin{displaymath} \frac{\partial}{\partial t}\left(\frac{\partial \rho u}{m}\right) +\frac{\partial \rho}{\partial x}=-Adv.U+Crv.U+Cor.U+Dif.U\end{displaymath}

\begin{displaymath} \frac{\partial}{\partial t}\left(\frac{\partial \rho v}{m}\right) +\frac{\partial \rho}{\partial y}=-Adv.V+Crv.V+Cor.V+Dif.V\end{displaymath}

Vertical Momentum Equations

\begin{displaymath} \frac{\partial}{\partial t}\left(\frac{\partial \rho w}{m}\r... ...\partial p}{\partial z}+\rho g\right) =-Adv.W+Crv.W+Cor.W+Dif.W\end{displaymath}

Pressure Equations

\begin{displaymath} \frac{\partial \rho}{\partial t}+m^2\left\{\frac{\partial}{\... ...rac{\partial}{\partial z} \left(\frac{\rho w}{m}\right)+Prc \\ \end{displaymath}

The left side terms related to sound mode are treated separately in time integration procedure and calculated with smaller time step. Other right side terms are considered with larger time step. Other procedures are quite similar to original MRI-NHM. Table 1 shows main specification of the dynamical scheme of the MRI/NPD nonhydrostatic model. We conducted simple tests of DFI(Digital Filtering Initialization) and we will introduce DFI to MRI/NPD-NHM in the near future. Physical processes are as same as in MRI-NHM.


Table 1: Specification of dynamical scheme of MRI/NPD nonhydrostatic model
Government equations Fully compressible equations
Horizontal coordinate Conformal coordinate
Vertical coordinate z*
Horizontal gridding Arakawa C
Vertical gridding Lorenz
Time Integration (Treatment of sound mode) Split Explicit (HE-VI) or Semi Implicit (HI-VI)

3. Examples of simulation

a. Mountain wave

We performed simple tests of idealized mountain wave simulation. Figure 1 shows the vertical profile of vertical wind. The result from the HE-VI scheme of MRI/NPD-NHM is almost similar to that from HI-VI of the model in this case.


\begin{figure} \par \centerline{ \psfig {file=hevi.ps,height=2in} , \psfig {file... ...ountain wave simulation : HE-VI case (left) and HI-VI case (right).}\end{figure}

b. Real data forecast

Figure 2 shows an example of real-data simulation with MRI/NPD-NHM. The horizontal resolution of this simulation is 10km and lateral boundary condition is provided by the JMA operational regional model (RSM). MRI/NPD-NHM can predict rain-band cloud cluster and severe rainfall in this case, though RSM tends to simulate wider rainfall area and smaller amount than observation. 10km may be still coarse for mesoscale model for preventing natural disaster and 10km mesh model with micro physical processes could not resolve all cumulus convection in severe rainfall areas. Data assimilation is not involved in this simulation yet. We don't expect higher skill of nonhydrostatic model in this experimental stage.


\begin{figure} \par \centerline{ \psfig {file=nhm06.ps,height=2in} , \psfig {fil... ...evel (20m from the surface). (right): Same as left one but for MSM.}\end{figure}

4. Future Plan

One of major issues of MRI/NPD-NHM is computational cost for operational usage. We'll optimize the source code and improve efficiency. Goal of this project is to achieve mesoscale numerical weather prediction system which contains data assimilation procedure, forecast model, other pre and post procedures and so on.

5. References

Saito, K., 1997 : Semi-implicit fully compressible version of the MRI mesoscale nonhydrostatic model - Forecast experiment of the 6 August 1993 Kagoshima torretial rain. Geophys. Mag. Ser. 2, 2, 109-137.

*Corresponding author address:

Dr. Chiashi Muroi
Numerical Prediction Division
Japan Meteorological Agency
1-3-4 Ote-machi, Chiyoda-ku, Tokyo, 100-8122, Japan
E-mail: cmuroi@npd.kishou.go.jp