**3.5.1 Mesoscale assimilation of GPS data**

Water vapor is one of the most important parameters in weather forecasting, and GPS is a powerful tool for retrieving accurate water vapor information. In Japan, the Geospatial Information Authority of Japan has been operating a nationwide permanent dense GPS array, the GPS Earth Observation Network (GEONET), since 1994. Shoji (2009) developed a near real-time (NRT) analysis system of TPWV derived from GEONET data to contribute to water vapor monitoring and NWP. Ishikawa (2010) applied this system to the operational GPS TPWV data assimilation at JMA using JNoVA and contributed to improve the MSM's QPF performance (see 2.2.4).

On 28 July 2008, a local heavy rainfall occurred over the Hokuriku and Kinki districts, central Japan. Shoji et al. (2009) used Meso 4DVAR to perform data assimilation experiments of GEONET TPWV data for this event, and demonstrated that the rainfall forecast was improved. Further improvements were obtained by adding TPWV derived from GPS stations of the International GNSS Service in Korea and China.

Seko et al. (2010) used the Meso 4D-Var system for a heavy rainfall event in northern Japan on 16 July 2004 to investigate the impacts of three kinds of GPS-derived water vapor data: TPWV, slant water vapor along the path from the GPS satellite to the receiver (SWV), and radio occultation (RO) data along the path from the GPS satellite to the CHAllenging Minisatellite Payload (CHAMP) satellite. When SWV and RO data were assimilated simultaneously, both the rainfall region and rainfall amount were similar to the observed ones.

The JMA Nonhydrostatic Model and Its Applications to Operation and Research 99

Another reason of difficulty in predicting local heavy rainfall is the inherent low predictability of severe small-scale phenomena, that occur under convectively unstable atmospheric conditions. To consider forecast errors due to uncertainties in initial conditions and numerical models, ensemble prediction systems (EPSs) are widely used for medium

Seko et al. (2009) conducted 11-member mesoscale ensemble experiments using NHM with a horizontal resolution of 15 km for two tornado events in Japan. Initial conditions were produced by adding the normalized perturbation of operational one-week ensemble forecast of JMA. Probabilities that the Energy Helicity Index (EHI) exceeds some criteria were examined, and feasibility of the probability forecast of tornadoes using the EPS-

As discussed in 3.2.3, Saito et al. (2010a) conducted ensemble predictions of Nargis and the associated storm surge. NHM with a horizontal scale of 10 km was used for the 21 member ensemble prediction. In addition to the initial perturbations, the effect of lateral boundary perturbations (LBPs) on tropical cyclone ensemble prediction was examined. When LBPs were implemented, the ensemble spread increased by 50%, and root mean square errors

A mesoscale singular vector (MSV) method was developed by Kunii (2010a). The tangent linear model and the adjoint model of NHM developed for JNoVA (Honda et al., 2005) were used in the Lanczos method with Gram-Schmidt re-orthogonalization to obtain the singular vector. Kunii (2010b) tested the MSV for a heavy rainfall event to assess MSV performance as the initial perturbation method. A torrential rainfall that occurred over central Japan on 29 August 2008 (Fig. 3a) was chosen. Ensemble forecast with a horizontal resolution of 15 km was conducted, where probabilistic values were determined by the proportion of members that predicted precipitation above a certain threshold. A greater-than-30% probability of precipitation was estimated even with the large threshold of 50 mm/3 hours (Fig. 3c), whereas the control forecast (Fig. 3b) predicted rainfall of only about 20 mm/3

Fig. 4. a) 3-hour accumulated precipitation at 1800 UTC 28 August 2008 (Radar AMeDAS analyzed rainfall). b) Rainfall predicted by a control forecast (FT = 06). c) Probability forecasts

Kunii and Saito (2009) conducted a sensitivity analysis experiment using MSV to support the THORPEX Pacific Asian Regional Campaign (T-PARC). For TY0813 (SINLAKU), MSVs-

of 3-hour accumulated precipitation with a threshold of 50 mm. After Kunii (2010b).

range NWP, and there is now an increasing need to develop mesoscale EPSs.

(RMSEs) of the ensemble mean forecast became smaller than without LBPs.

**a) b) c)** 

**3.5.3 Mesoscale ensemble prediction** 

derived potential parameters was indicated.

hours.

#### **3.5.2 Storm scale 4DVAR**

Although JNoVA contributed to improve the QPF performance of operational MSM, its horizontal grid spacing in the inner loop model is 15 km and only large-scale condensation is considered in the adjoint model. Kawabata et al. (2007) developed a cloud-resolving 4DVAR system based on the JMA-NHM (NHM-4DVAR), and applied it to reproduce the deep convection observed in Tokyo on 21 July 1999. The cost function to be minimized was formulated as

$$f(\mathbf{x}\_0) = \frac{1}{2} (\mathbf{x}\_0 - \mathbf{x}\_0^{\circ})^\mathrm{T} \mathbf{B}^{-1} (\mathbf{x}\_0 - \mathbf{x}\_0^{\circ}) + \frac{1}{2} (\mathbf{H}\mathbf{x} - \mathbf{y}^{\circ})^\mathrm{T} \mathbf{R}^{-1} (\mathbf{H}\mathbf{x} - \mathbf{y}^{\circ}), \tag{18}$$

where *x* denotes the model prognostic variables, subscript 0 means those at the beginning time of the assimilation window, and *x0 <sup>b</sup>* is the first guess of *x0*. **B** represents the background error covariance matrix. *H* is the observation operator, *yo* is the observations, and **R** the observation error covariance matrix. Lateral boundary conditions were also included in the analysis. The adjoint model included only dry dynamics and advection of water vapor, but they successfully reproduced observed cumulonimbi by assimilating Doppler radar radial winds and GPS TPWV data. This study was the first to demonstrate the feasibility of shortrange forecasting of local heavy rainfall brought about by deep convection, using a full-scale numerical model and a dense observation network.

Kawabata et al. (2011) implemented the warm rain process into NHM-4DVAR and applied it to a data assimilation experiment of a heavy rainfall event in Tokyo on 5 September 2005 with a horizontal resolution of 2 km. GPS-TPWV data was assimilated at 5-min intervals within the 30-min assimilation windows, and surface in-situ data and wind profiler data were assimilated at 10-min intervals. Doppler radial winds and radar-reflectivity data were assimilated at 1-min intervals. The 4DVAR assimilation reproduced a line-shaped mesoscale convective system (MCS) with a shape and intensity consistent with the observation (Fig. 3). Assimilation of radar-reflectivity data intensified the MCS and suppressed false convection.

Fig. 3. Three-dimensional image of the MCS in Tokyo on 5 September 2005 reproduced by NHM-4DVAR.
