**4. Summary**

The horizontal distributions of rainfall in A\_ZTD and A\_PWV (**Figure 11c** and **d**) were close to each other. In A\_SPD (**Figure 11b**), the initiation of intense rainfall enhanced over southern Okinawa at 1200 JST, and the maximum intensity reached 47 mm h−1 (not shown). By 1300 JST, a rainband had formed over the island, and the distribution and intensity resembled the radar observation (**Figure 11a**). Therefore, it can be concluded that the assimilation of SPD data showed improvement of the rainfall forecast with respect to both timing and intensity compared with the assimilation of PWV and ZTD data. This improvement was obtained through modifications in the atmospheric profile in the simulation after the SPD assimilation (not shown).

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156 Multifunctional Operation and Application of GPS

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**Figure 11.** Horizontal distribution of 1-h accumulated rainfall amount between 1300 and 1400 (FT = 02) JST. (a) Radar

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observation, (b) A\_SPD, (c) A\_ZTD and (d) A\_PWV. Modified Figures 2 and 15 of Kawabata et al. [4].

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GNSS analysis is performed with a number of models for solid earth tide, ocean tide, earth rotation, and atmospheric delay. However, conventional GNSS analysis inevitably has errors caused by local-scale variations in the atmosphere, even if estimates of the gradient parameters are applied. These errors affect positioning as well as atmospheric delays. Spatial correlation in screened post-fit phase residuals (i.e., the higher order inhomogeneity part) must be caused by local-scale variations in the atmosphere, which are not resolved by ordinary ZTD and gradient parameter analysis. Thus, GNSS postfit residuals can be used to detect the inhomogeneous distribution of water vapor on a local scale of less than 10 km caused by weather disturbances like convective thunderstorms. In this chapter, we introduced two new indices and one experimental method to retrieve a several-kilometer-scale PWV distribution. These approaches may be a preliminary way to serve operational monitoring of cumulus convection.

Currently, multiple GNSSs (e.g., the Russian GLONASS, EU's GALILEO, China's BeiDou, and Japan's Quasi-Zenith Satellite System (QZSS)) can serve to more precisely resolve localscale water vapor variation. In addition, the advancement of real-time GNSS analysis has been progressing rapidly. Real-time orbit and clock corrections have offered officially by the International GNSS Service (IGS) since April 2013. Moreover, a Multi-GNSS orbit and clock estimator called MADOCA (Multi-GNSS Advanced Demonstration tool for Orbit and Clock Analysis) has been developed by the Japan Aerospace Exploration Agency (JAXA) and they started to provide real-time ephemerides via the Internet (https://ssl.tksc.jaxa.jp/madoca/public/public\_index\_en.html) in September 2015. These rapid advancements in GNSS technology should speed the reality of new usage of GNSS-derived SPD.

Another application of SPD data at a local scale is data assimilation (DA). As shown in this chapter, a promising avenue for DA applications is to improve the initial conditions of a numerical weather model in high-resolution simulations. NHM-4DVAR with a 2-km horizontal grid spacing was used for assimilating GNSS slant path delay data. Compared with simulations after assimilating PWV and ZTD data, the assimilation of SPD showed inhomogeneous increments. Moreover, the analysis increments in the assimilation of SPD at low altitudes were larger than in the others. Conducting actual observation assimilations, the SPD assimilation clearly improved the forecast of both the timing and intensity of the rainband. This improved forecast was given through the decreased atmospheric stability over Okinawa Island.

The SPD data include information on temperature, dry atmospheric pressure, and water vapor pressure. In addition, the data contain both horizontal and vertical information on those atmospheric parameters. Because atmospheric inhomogeneity is greatest in the lower troposphere, assimilating SPD data is a promising way to improve forecast of a rainband. A GNSS signal along a path with a 15° elevation angle propagates about 11 km in horizontal and travels 3 km in vertical. Therefore, it is concluded that data assimilation systems at storm scales like used in this study are necessary to assimilate SPD data for taking advantages.
