On the Use of the Ensemble Kalman Filter for Torrential Rainfall Forecasts

Abstract

Torrential rainfall is a threat to modern human society. To prevent severe disasters by the torrential rains, it is an essential to accurate the numerical weather prediction. This article reports an effort to improve torrential rainfall forecasts by the Ensemble Kalman Filter based on the recent studies. Two series of numerical experiments are reported in this chapter. One is a dense surface observation data assimilation for a disastrous rainfall event caused by active rainband maintained for a long time. Although an experiment with a conventional observation data set represents the rainband, the significant dislocation and the underestimated precipitation amount are found. By contrast, dense surface data assimilation contributes to improve both the location and surface precipitation amount of the rainband. The other is the rapid-update high-resolution experiment with every 30-second Phased Array Weather Radar (PAWR) data for an isolated convective system associated with a local torrential rain. The representation of this event is completely missed without the PAWR data, whereas the active convection is well represented including fine three-dimensional structure by PAWR data assimilation. Throughout these studies, the data assimilation by Ensemble Kalman Filter has a large positive impact on the forecasts for torrential rainfall events.

1. Introduction

The torrential rainfall is becoming one of the most significant treats in worldwide human society year by year. It often brings severe disaster in social infrastructure or human lives. In Eastern Asia, the disasters caused by heavy rainfalls are repeated as every year. In Japan, many rainfall events have brought severe disasters especially in summer season. Among them, in September 2015, active rainband maintained in eastern part of Japan for several days, and severe flood happened. Eventually, it caused 20 fatalities and more than 7000 house damages [1]. In July 2018, a record-breaking and catastrophic torrential rainfall occurred over a wide area of western Japan. According to a report by Fire and Disaster Management Agency, Japan, it caused 263 fatalities, 484 injuries, and more than 30,000 home damages [2]. In another case, the monsoon front so-called Baiu front (in Japanese) or Meiyu front (in Chinese) remained stagnant for long time in July 2020, large amounts of water vapor tended to flow into the Japan islands. This caused record-breaking rainfall over a wide area of Japan. Especially in Kumamoto prefecture located southwest part of Japan, floods of unprecedented magnitude occurred [3, 4, 5, 6]. Besides these events, sudden local torrential rainfalls also often happened in summer season. On September 11, 2014, an isolated cumulonimbus suddenly developed within 10 minutes, and over 50 mm h⁻¹ intense rainfall was observed, even though it was sunny until then. Recently, even in Europe, where climatological annual rainfall amount is relatively low, less than 1000 mm per year, the occurrence of torrential rains is not unusual. For example, the ECMWF reported extreme rain in Germany and Belgium in July 2021 [7].

To reduce disasters caused by severe rainfall events, a development of an accurate numerical weather prediction (NWP) system is essential. To improve the forecast accuracy, more accurate initial conditions are needed. Accurate initial values can be obtained through advanced initial value creation methods that maximize the use of information from observations, and data assimilation plays a central part in it. In modern NWP system, variational method and Kalman Filter, especially Ensemble Kalman filter [8], are widely applied. Although both schemes have their advantages and disadvantages, Ensemble Kalman Filter is generally superior to implementation and maintenance [9]. The reason why Ensemble Kalman filter rather than the traditional Kalman filter is applied in the NWP is the computational cost. It is quite difficult to apply the traditional Kalman filter technique due to the huge computational cost mainly in the estimation of error covariance matrix. The NWP models has very large degree of freedom, and it usually consists over 10⁷ grid points and over 10 variables. On the other hand, in Ensemble Kalman Filter, since error covariance matrix is estimated from the ensembles of the order of 10–100, it is expected to significantly reduce computational costs. In this chapter, the author reports recent studies of improving the torrential rainfall forecasts. In Section 2, an impact of dense surface data assimilation on the forecast of band-shaped rainfall zone is presented. In Sections 3 and 4, the importance of rapid-update data assimilation for a local torrential rainfall having the order of 10 km or less and a practical application for the forecast are presented. In Section 5, the conclusion is described.

2. The dense surface observation data assimilation for a forecast of a torrential rainband

2.1 Introduction

In the torrential rainfall event in Japan, band-shaped rainfall areas are often observed. In Japan, it is widely called “Senjo-Kousui-Tai,” an example of translation is “linear rainband.” According to an explanation by JMA, this type of rainband is explained as follows: a rainfall area with intense precipitation extending in 50–300 km length and 20–50 km width, created by organized cumulonimbus clouds, which are formed by a series of developing rain clouds passing or lingering in the same location for several hours [10]. As the development of observational networks, torrential rainbands are frequently captured, and they are one of the most essential factors in severe meteorological disasters. In this section, a record-breaking rainfall event in Kanto, Tohoku region, which is located in eastern Japan, in September 2015, is focused. In this event, the southerly winds from Typhoon No. 18, made landfall in the central region of mainland of Japan and moved into the Sea of Japan. At about the same time, the southeasterly winds from Typhoon No. 17 moved northward in Pacific Ocean over the eastern Honshu region. This moist air mass flowed into the Kanto and southern Tohoku regions. The air mass maintained a pronounced convergence zone for a long time, resulting in the development of a series of torrential rain bands. Eventually, the accumulated precipitation since the beginning of the rainfall reached 647.5 mm, more than twice the monthly precipitation normal for September. In addition, 16 of the JMA’s 1300 surface observation stations (Automated Meteorological Data Acquisition System; AMeDAS) recorded the highest maximum 24-hour precipitation in observation history [11, 12].

The active rain band itself had a scale of several hundred kilometers; however, the peak precipitation, which directly related to severe disasters, was concentrated in a narrow region. From the viewpoint of heavy rainfall forecasting and disaster prevention, it is desirable not only to improve the accuracy of simulation of a 100 km-scale phenomenon, but also to be able to simulate particularly intense local precipitation with pinpoint accuracy in terms of both location and amount. In this section, as a modern NWP study, a series of data assimilation experiments with dense surface observation data for the heavy rainfall event in September 2015 are reported. The surface observation data comes from the Environmental Sensor Network provided by NTT DoCoMo, which is a major mobile phone company in Japan, and it has about 4000 stations throughout Japan. This observation network has approximately 5-km special intervals and 1-minute temporal resolution at minimum. This study focuses on the impact of this dense surface observation data on the forecast for the rainfall.

2.2 Experimental design

This series of experiments was performed by an NWP system called SCALE-LETKF [13]. It combines the Local Ensemble Transform Kalman Filter (LETKF)[14] with a regional numerical model Scalable Computing for Advanced Library and Environment (SCALE) [15].

The workflow is visualized in Figure 1. Firstly, 18-km-mesh model with 271x243x50 grid points, 6-hour-update, 50-member SCALE-LETKF was performed from 0000 JST on September 7, 2015, to 0000 JST on September 10, 2015. Initial condition of ensemble mean and boundary condition came from National Center for Environmental Prediction, Global Forecast System (NCEP GFS). The initial perturbation for generating initial ensemble state came from the perturbation components of NCEP Global Ensemble Forecast System (GEFS). The assimilated observation data are NCEP PREPBUFR. It consists conventional observation by airplanes, ships, buoys, satellites, surface stations, radiosondes. The locations and elements of the observation are summarized in Figure 2 and Table 1; however, some observation systems such as the orbital satellites, airplanes, and ships are not stationary. Thus, it needs to pay attention that the locations in Figure 2 are just an example at a single time. Next, 4-km-mesh, hourly update data assimilation experiments were performed. The initial ensemble states were interpolated from 18-km-mesh data at 0000 JST on September 7, 2015. The hourly boundary conditions came from a simple forecast at 18-km resolution initialized at 0000 JST on September 7, 2015. To investigate impacts of rich surface observation data, two experiments were performed. One experiment only assimilates NCEP PREPBUFR (CTRL). Although NCEP PREPBUFR is delivered every 6 hours, it has been divided into hourly segments with reference to time stamps for the hourly update LETKF cycles. The other assimilates rich surface observation data in addition to NCEP PREPBUFR (TEST). The surface data have been interpolated to the nearest numerical model grid point by bilinear scheme in horizontal and been applied an altitude correction using moist-adiabatic lapse rate in vertical as an observation operator for data assimilation. The surface stations observe wind velocity, pressure, temperature, relative humidity, rainfall amount, solar radiation, and detection of precipitation. In this experiment, wind velocity, pressure, temperature, and relative humidity were assimilated.

Figure 1.

The workflow of the data assimilation experiments. NCEP PREPBUFR was input both in CTRL and TEST, and surface observation was input in TEST only.

Figure 2.

An example of the observation sites of NCEP PREPBUFR. The valid time is 1200 UTC on December 1, 2019. (a) Aircraft observations, (b) satellite-assigned atmospheric tracking winds, (c) satellite scattered measured winds, (d) surface observations, (e) ship and buoy observations, and (f) radiosonde observations, respectively.

(a) AIRCFT	Aircraft observations	Horizontal wind [m s^−1], Temperature [K], Pressure [hPa] Specific humidity [kg kg^−1], Geopotential height [m]
(b) SATWIND	Satellite-assigned atmospheric tracking winds	Horizontal wind [m s^−1], Pressure [hPa]
(c) ASCATW	Satellite scattered measured winds	Horizontal wind [m s^−1], Geopotential height [m]
(d) ADPSFC	Surface observations	Horizontal wind [m s^−1], Temperature [K], Pressure [hPa] Specific humidity [kg kg^−1]
(e) SFCSHP	Ship and buoy observations	Horizontal wind [m s^−1], Temperature [K], Pressure [hPa] Geopotential height [m]
(f) ADPUPA	Radiosonde observations	Horizontal wind [m s^−1], Temperature [K], Pressure [hPa] Specific humidity [kg kg^−1], Geopotential height [m]

Table 1.

Observation elements in the NCEP PREPBUFR. The elements enumerate all the data stored in the files, including those that are diagnostically calculated.

2.3 Result and discussion

2.3.1 Result of the analyses

Firstly, the difference of relative humidity between CTRL and TEST after the first data assimilation cycle is shown in Figure 3. The impact of surface data is clearly appeared, and positive values are widespread. In this case, numerical model underestimated the surface relative humidity; in other words, it predicted drier condition. However, owing to the dense surface data assimilation, the lower relative humidity was well modified.

Figure 3.

The difference of surface relative humidity between TEST and CTRL after the first data assimilation cycle at 0100 JST, September 7.

Next, the rain mixing ratios [g kg⁻¹] at the lowest model level (approximately 20-m altitude) at 1200JST and 1800 JST on September 9, 2015, are shown in Figure 4 This period corresponds to observing the intense precipitation by gauge observation around the disaster area. In both cases, peak rainfall mixing ratios reached the order of 1 g kg⁻¹, indicating that intense precipitation is occurring. However, in a quantitative comparison, particularly intense precipitation areas above 2 g kg⁻¹ are only found in TEST. Focusing on the distribution of rain mixing ratio, the CTRL shows a northwesterly tilt of the precipitation zone. In CTRL, the path of typhoon No. 18, which brought rich moisture into the disaster area, had westerly bias, so the moist air mass from the typhoon No. 18 flowed into the different area from the actual observation. In TEST, the issue of shifting to the west remains; however, precipitation area extended in meridional direction, and it has consistency with the actual phenomenon. The dense surface data assimilation contributed to reproduce the distribution and amount of rain mixing ratio closer to reality than CTRL.

Figure 4.

Rain mixing ratio of the ensemble mean analyses at (a1, b1) 1200 JST, September 9, and (a2, b2) 1800 JST, September 9. Top and bottom rows correspond to TEST and CTRL, respectively.

2.3.2 Forecast experiment

Here, 6-hour forecasts initialized at 1200 JST and 1800 JST were performed. The initial conditions come from the analyses of the ensemble mean of CTRL and TEST at each initial time. Figure 5 shows 6-hour accumulated precipitation amount [mm] of the forecasts. For reference, analysis precipitation, which is the best estimation of surface precipitation intensity at 1-km resolution by JMA, is also shown. In CTRL, regardless of the initial time, the precipitation area is shifted about 100 km to the west compared with the JMA analyses. Moreover, accumulated precipitation amount in CTRL was underestimated. At 1800 JST, even though the peak precipitation amount was 80% level of the JMA analysis, a quite narrow rainband was represented. In TEST, dislocation of the precipitation areas was improved and quantitatively consistent with JMA analyses.

Figure 5.

Six-hour accumulated precipitation amount [mm] in the forecasts initialized at (a) 1200 JST, September 9 and (b) 1800 JST, September 9.

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.

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, 18, 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].

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.

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, 21, 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 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:

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.

$$\text{dBZ}=10\times {\log }_{10}\left\{\left(2.53\times 10^4\right){\left(\rho \text{QR}\right)}^{1.84}+\left(3.48\times 10^4\right){\left(\rho \text{QS}\right)}^{1.66}+\left(8.18\times 10^4\right){\left(\rho \text{QG}\right)}^{1.50}\right\}$$E1

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 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.

4. The importance of rapid-update Kalman filtering for the local torrential rainfall

This section provides an explanation of the importance of rapid-update Kalman Filtering for the local torrential rainfall. Here, the “local” refers to a special scale of the order of 10 km or less.

In the first place. The weather system has strong nonlinearity, and the error grows exponentially as the time progresses. Moreover, the weather system has multiscale structure. Large-scale phenomena such as jet stream and have slower error growth, whereas the smaller special scale phenomena have the faster error growth. In torrential rainfalls, cumulus convection plays a main part, and it is the key issue that how to accurately estimate the state of cumulus convection. A relation between special scale and predictive skill is well described in Forecast User Guide by ECMWF [27]. According to Figure 7(b1) in the document by ECMWF [27], cumulus convection has 1-km order special scale, and it develops within 10 minutes; thus, fine temporal resolution is required to capture the developing process of the cumulus convection. Recently, sensing technologies have been exploring, and they also have been applied to weather observation instruments, such as radars or satellites. An example of the observation of the cumulus convection has already shown in Figure 6. Here, let us see the rapid growth of a convective system in Figure 6, carefully. At 0805 JST, only weak radar echo is found. It is a signal of the initiation of rainfall system (Figure 6a). At this time, the rainfall intensity is about only 1 mm h⁻¹. The minute-by-minute observation appears to be continuously changing (Figure 6a–d). However, this system rapidly evolved within 10 minutes, an active convection having the intense precipitation was formed by 0815 JST (Figure 6f).

As mentioned in Section 1, the data assimilation has become an important technique, and Kalman filter is widely applied to convective-scale weather forecasts. The important issue in Ensemble Kalman filter is how to set the length of the data assimilation window. In the first place, Kalman filter assumes linear theory. To apply it to the nonlinear system such as NWP model, we assume that a linear approximation holds within one data assimilation window. So, setting too long assimilation window will destroy the assumption of a linear approximation, resulting in a significant reduction in estimation accuracy. It is repeatedly mentioned that an active convection system, which brings a torrential rainfall, rapidly develops within 10 minutes or so [27] (Figure 6). Thus, short-time data assimilation window should be taken in case of applying the ensemble Kalman Filter to torrential rainfall forecast. Here, how long should the data assimilation window be short? Now, let us see Figure 6 again. Even though the convective cloud is rapid growth system, it can be considered linear growth within a few minutes range. Of course, the shorter the time progress, the more linearity is ensured. From the perspective of Ensemble Kalman Filter, the shorter data assimilation window is taken, the higher accuracy is expected, because the Kalman Filter assumes linear theory. On the other hand, the computational cost will explosively increase by the very short window; however, this issue has been overcome with the innovation of supercomputers. In the previous sections, the author reported a 30-second-update data assimilation experiments for a torrential rainfall event by the previous Japanese flagship supercomputer “K” based on the contents of a published paper. Recently, more powerful supercomputers, such as the current Japanese flagship supercomputer “Fugaku,” are operated all over the world. With the development of supercomputers, more accurate NWP system will be performed in operation.

5. Conclusion

This chapter presented the investigations of the forecasts in several torrential rainfall events using Ensemble Kalman Filter. These descriptions are based on my recent studies [17]. In Section 2, I aimed to investigate the impact of dense surface observation data on a hazardous rainfall event in eastern Japan area in September 2015. In this case, a convergence zone extending in meridional direction was maintained by the surrounding wind of two typhoons. It associated to activate the rainband and cause a record-breaking precipitation. So, an impact on the rainband was the primary focus of the study. In this study, two data assimilation experiments were performed. Although the conventional data set (NCEP PREPBUFR) has many kinds of observations, it is difficult to perform precise forecast for the torrential rain. In addition to it, dense surface observation data assimilation contributed to improve forecast accuracy in both rainfall area and amount. Surface observation network is a classical system compared with modern remote sensing instruments. Even though total data size from 4000 stations is the order of 100 kB at one observation time, its data assimilation has certain impact on a torrential rainfall forecast having horizontal scale of the order of 100 km. Sections 3 and 4 showed that the rapid-update data assimilation can be a powerful tool in forecasting a local torrential rainfall through a single case study. In Section 3, a rapid-update ensemble Kalman filtering study 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. Since the local convective system having 10-km or less special scale grows within 10 minute. The conventional forecast system, which has 1-hour or longer data assimilation cycles and 1-km order horizontal resolution, has hardly resolved an isolated convective system both especially and temporary. To address this issue, 30-second-update, 100-m-mesh experiment was performed. Owing to the innovative NWP system, the torrential rain by an isolated convective system was well represented including its three-dimensional structure, and forecast accuracy was clearly improved. In Section 4, in general, these results were investigated by case studies. As mentioned in Section 3, several issues remained especially in the 100-m-mesh forecast. In order to contribute the results of the research to improve forecasts universally, additional experiments should be conducted and profiled the issues. Moreover, to review the entire parameter settings in Ensemble Kalman Filter is also important.

Acknowledgments

The author thanks the research scientists of data assimilation for the weather forecast, especially the authors of cited papers and websites. Also, the author thanks Ms. Silvia Sabo and Ms. Martina Scerbe, who are the author service managers for a great support of the author’s writing activity. In the visualization, free software, the Grid Analysis and Display System (GrADS) developed by Center for Ocean-Land-Atmosphere Studies, Institute of Global Environment and Society, George Mason University, was used.