## 3 Estimation Methods and Techniques  
### Statistical Application  
Rainfall measured using several rain gauges and radar or weather satellite sensing can be used to estimate average rainfall in an area at a specific time interval. Moreover, the estimation method can be classified into two categories based on whether it uses rain gauge  
Figure 4: Satellite imagery depicting atmospheric conditions in one region of Indonesia during high rainfall intensity: (**a**) rainfall during floods in Sidoarjo City, (**b**) time series graph of cloud peak temperature, red box shows the time of occurrence during floods and (**c**) cloud phase distinction RGB satellite imagery product. The yellowish color signifies a thick and high cloud containing ice particles. Red circle shows the location of Sidoarjo City (modified from [67]). Figure 5: Parallax correction (in km) of Himawari-8 satellite based on cloud-top height of 15 km for the entire Territory of Indonesia. Cloud-top height in convective clouds is an essential feature in extreme weather nowcasting performed by weather forecasters to represent the core location of the severe region of the convective cloud (modified from [88]). data or radar-based or weather-satellite-based estimation. Both estimation approaches are illustrated in Figure 6.  
Data from a single rain gauge cannot represent rainfall in a given area. Thus, rainfall data from several rain gauges located throughout the area are required [90, 91]. Furthermore, spatial data interpolation methods are required to estimate rainfall around known points. To generate spatially distributed rainfall fields, several interpolation methods for rain gauge points have been applied, including Thiessen polygon, inverse distance weighting, linear spline, and kriging [92, 93], as shown in Table 2. With their respective advantages and disadvantages, these methods have been implemented for case studies in Indonesia [94, 95, 96]. The results showed that spatial interpolation of rain gauge data is necessary to estimate rainfall, especially in Indonesia, in order to overcome data limitations and environmental and other physiographic conditions. Due to the complexity of the topography and geography in Indonesia, the choice of interpolation method for estimating rainfall is very important. However, selecting the optimal interpolation method must also consider the unique characteristics of each region more specifically. In addition, interpolation methods that only use rain gauges as data sources must incorporate data from other sources [97]. This is because combining multiple rainfall data sources, such as rain gauges, weather radar, and weather satellites, can provide more accurate rainfall estimates [98]. Figure 6: Rainfall estimation approaches using (**a**) rain gauges and (**b**) radar or weather satellite methods (modified from [89]). The correlation between weather radar reflectivity data and rainfall intensity data from rain gauges produces an empirical equation of the Z-R relationship [20, 103]. Modifications to the empirical equation constant have been applied for rainfall estimation in several Indonesian regions [104, 105, 106]. As a result, each study region has a distinct Z-R equation that can produce rainfall estimates with good statistical indicators. One study demonstrated that the relationship between radar reflectivity and rainfall can be developed using three different techniques: the traditional matching method (TMM), the probability matching method (PMM), and the window probability matching method (WPMM), as shown in Figure 7. The results revealed that PMM and WPMM provided a better relationship than TMM [24]. Statistical methods can be used to validate satellite data using rain gauges [107, 108, 109, 33] or weather radar measurement methods [111, 112, 113, 114]. In the case of validation using rain gauges, it is important to consider the number and distribution of rain gauges, as these factors can significantly influence the estimation results.