**3. The rapid-update Kalman filtering for a torrential rainfall event**

#### **3.1 Introduction**

This section reports a study of rapid-update ensemble Kalman filtering for a torrential rainfall event on September 11, 2014, in Kobe city, which locates in the western part of Japan and provides a discussion of an impact on a torrential rainfall forecast.

#### **Figure 6.**

*Zonal-vertical cross section of the radar reflectivity [dBZ] of an isolated convective system generated around Kobe city on September 11, 2014. (a) 0805 JST, (b) 0806 JST, (c) 0807 JST, (d) 0808 JST, (e) 0810 JST, (f) 0815 JST, (g) 0820 JST, (h) 0825 JST.*

In this case, an isolated convection system suddenly occurred near Kobe City. **Figure 6** shows a developing process of the cumulonimbus, which was captured by an innovative meteorological observation instrument called phased array weather radar (PAWR) located at Osaka University, Suita city, Osaka, Japan [16]. The PAWR enables to observe a range of 60-km radius with approximately 100-m special resolution and 30-second time resolution. Although it has not been used for the operational weather forecast yet, it has been utilized for a lot of research of the NWP [5, 17–19]. Also in this event, the PAWR at Osaka University [16] well captured the convective initiation and developing process with very high special and temporal resolution. The PAWR observed the first echo at 0758 JST, and its intensity was at most 1 mm h−1 in terms of surface precipitation. However, at 0808 JST only 10 minutes later, it was up to 50 mm h−1. Despite the occurrence of torrential rain, the operational forecast completely missed this event. It is because the operational NWP system has not been designed for such an isolated convective system so far. Although this event did not bring the large-scale disaster such as a flood or a landslide, it was a case of social impact. Many people mourned on SNS that they were hit by a sudden heavy rain during the commuting time because the weather forecast on the morning of the day did not broadcast the rainfall forecast. The failure prediction could be attributed that both horizontal resolution and data assimilation window of the operational NWP systems did not match for the local-scale phenomena. To fix this issue, fine resolution and rapid data assimilation cycles are required in the NWP system. Toward forecasting such a torrential rainfall, this study tried to perform 30-second-update, 100-m-mesh data assimilation experiment. This study aims to investigate the impact of such a high-resolution and rapid-update NWP system on the forecast of an isolated convective system. The descriptions in this section are based on a part of a published journal article [17].

### **3.2 Experimental settings**

Here, general settings of a series of data assimilation experiment are described. For details, see the original paper [17].

This series of experiments used the Japan Meteorological Agency nonhydrostatic model (JMA-NHM)[20–22] implementing LETKF [14]. This NWP system is called NHM-LETKF [23, 24]. JMA-NHM was used as the operational mesoscale NWP model in JMA until February 2017. The numerical experiment took quintuple downscaling

#### *On the Use of the Ensemble Kalman Filter for Torrential Rainfall Forecasts DOI: http://dx.doi.org/10.5772/intechopen.107916*

strategy. First, 15-km-mesh, 6-hour-update, 100-member NHM-LETKF was performed for 10 days from 0900 JST September 1, 2014. The initial and boundary conditions were JMA global spectrum model (GSM) initialized at 0900 JST September 1, 2014, and the perturbations among the ensemble members came from forecast data by JMA global ensemble prediction system (GEPS) initialized at the same time.

Next, 5-km-mesh and 1-km mesh ensemble simulations initialized by the result of the15-km-mesh run were performed. The result of 1-km-mesh ensemble run provided the initial and boundary conditions for the following data assimilation experiments. In the main experiments, 100-m-mesh, 30-second-update LETKF with every 30-second PAWR observation data was cycled (100 M). To discuss the dependence of horizontal resolution, 1-km-mesh, 30-second-update LETKF was also cycled (1 K). These main experiments were performed from 08:00 JST to 08:30 JST on September 11, 2014, and they provided every 30-second, 100-m-mesh, 100-member analysis data. For reference, a similar experiment but without inputting any observation was performed (NO-DA).

Following the series of data assimilation experiments, 30-mitute forecasts initialized by the ensemble-mean analyses at 0830 JST were performed to evaluate the impacts on the torrential rainfall forecasts.

#### **3.3 Result and discussion**

To evaluate the impact of every 30-second PAWR data assimilation on the precipitation, the ensemble-mean analyses of the radar reflectivity (dBZ) at 0830 JST corresponding to the last data assimilation cycle are shown in top panels of **Figure 7**(a0-d0). Although the numerical model does not predict the radar reflectivity directory, it can be calculated by the observation operator applied in the PAWR data assimilation experiment as follows:

$$\text{dBZ} = \text{no} \times \log\_{10} \left( \left( \text{2.53} \times \text{10}^4 \right) \left( \rho \text{QR} \right)^{\text{1.84}} + \left( \text{3.48} \times \text{10}^4 \right) \left( \rho \text{QS} \right)^{\text{1.66}} + \left( \text{8.18} \times \text{10}^4 \right) \left( \rho \text{QG} \right)^{\text{1.59}} \right) \quad \text{(1)}$$

where ρ, QR, QS, and QG are air density [kg m−3], mixing ratios of rain, snow, and graupel [g kg−1], respectively [25]. The mixing ratio means mass of particles in 1-kg of dry air.

In NO-DA, the entire area is less than 15 dBZ, which is visualized by white shade. The white-colored area can be assumed no precipitation; namely, we hardly find any convective initiations. Both in 1 K and 100 M, intense radar echo corresponding to the precipitation is created, and their locations are good agreement with the PAWR observation. However, the peak intensity of radar echo is significantly different between 1 K and 100 M. In 100 M, the center of the convections shown by over 45 dBZ is clearly found. By contrast, 1 K only shows 36 dBZ at the peak. This underestimation is critical to the reproducibility of the precipitation, because 45 dBZ in 100 M corresponds with over 23 mm h−1 of precipitation, whereas the precipitation intensity in 1 K only reaches about quarter level of that in 100 M. The time series of every 30-second analysis in 100 M was visualized in a three-dimensional movie, and it is available on YouTube: https://www.youtube.com/watch?v=s2PgH0mZ7G0 [26].

Below the second panels of **Figure 7** (a1-a3, b1-b3, c1-c3) show surface precipitation intensity at 0840, 0850, 0900 JST (10-, 20-, 30-minute forecasts) in NO-DA, 1 K, and 100 M, respectively. For verification truth, PAWR observation is shown in parallel (**Figure 7** d1–d3). While the PAWR observation shows intense echo of over 45 dBZ or more, the 1 K shows less than 35 dBZ. Moreover, in 1 K, the radar reflectivity

#### **Figure 7.**

*Radar reflectivity [dBZ] at 2-km elevation for (a0-a3) NO-DA, (b0-b3) 1 K, (c0-c3) 100 M and (d0-d3) PAWR observation. Top, second. Third and bottom rows correspond to 0830(initial time), 0840 (10-minute forecast), 0850 (20-minute forecast), 0900 JST (30-minute forecast), respectively.*

declined as the forecast progressed. In 100 M, both intensity of reflectivity and precipitation area show improvement (**Figure 7** c1–c3).

Here, one tendency of the forecast should be mentioned. In 100 M, after 20-minute from the start of the forecast (0850 JST), although precipitation intensity is consistent with the PAWR observation, the echo area appears to shift eastward. In 100 M, intense updraft over 20 m s−1 was generated and promoted excessive formation of ice crystals. The ice crystals are transported to the east by westerly general winds at about 4 -km level and fall as precipitation particles. That is a causation of the east-shift bias of the rainfall area. Toward performing more accurate forecasts, numerical scheme or model parameters mainly in cloud microphysics should be optimized for simulations with such a high resolution. Also, general simulation designs, such as downscaling strategy, model domains should be reconsidered in near future.

From these comparisons, the high frequency of data assimilation cycles and the very high horizontal resolution contribute to the creation of desirable initial values for forecasting the heavy rainfall. The importance of rapid update data assimilation cycle mentioned in Section 3 has been confirmed by this study. Even though 1-km resolution is fine horizontal grid spacing compared with the operational forecast systems, much higher resolution, which fully enables to resolve the active convections, has large advantage in the analyses and the forecasts.
