## 2 Materials and Methods
### Integrated Drought Monitoring with Multi-Sensor Based Statistical Simulations  
The types of RS data, mainly used for drought monitoring, depend on the type of satellite used; however, data such as precipitation, vegetation, surface temperature, soil moisture, and evaporation are mostly used. The data can be used individually. However, drought phenomena may not be sufficient for drought analysis based on a single indicator because it is related to a number of variables [34]. However, it may be more useful to combine information in the form of an appropriate drought index for more accurate monitoring of complex drought phenomena. [PERSON] and [PERSON] [23; 34] proposed the multivariate standardized drought index (MSDI) based on a copula distribution or nonparametric joint distribution for a bivariate model of precipitation and soil moisture. However, with recent advances in technology, the size and complexity of data tend to increase. Such complexity makes it difficult to detect the dependence between the response variable and covariates because of the enormous number of available covariates [35]. To resolve these problems, an approach to reducing the number of covariates (through dimension reduction) is being used. Principal component analysis (PCA) is a tool that is commonly used for dimension reduction [36] and is a feature transformation method that directly transforms the variables (in dimension reduction methods) without losing much of the data's inherent attribution information. In this study, for the three different multi-variables acquired from the satellite data, an integrated drought index is calculated through the application of the Bayesian PCA (BPCA; [37; 38]) and intentionally biased bootstrap (IBB; [39]) simulation for characterizing three aspects of meteorological (using SPI), agricultural (using ADCI), and hydrological (using WBDI) droughts. The BPCA approach can estimate the intrinsic dimensionality of the multi-dimensional dataset with missing data, which is suitable for application to satellite data, and has been evaluated as an accurate and robust model [37; 38; 40]. The BPCA analysis is performed by using the following three procedures: principal component (PC) regression, Bayesian estimation, and an expectation-maximization (EM)-like repetitive algorithm [38]. Figure 1: Geographical location of the five major river basins and the 849 sub-basins in Korea. The IBB applied for statistical simulation of drought indices is a kind of weighted bootstrap that follows constraints that are designed to select resampling probabilities and conditionally applied to data; this helps to improve the statistical performance and minimizes the distance of weighted distributions [39; 41]. This study employed the IBB to evaluate regional drought changes in meteorological (SPI), agricultural (ADCI), and hydrological (WBDI) droughs and analyzed the relative sensitivity of each drought index to the RS-based integrated drought index (RSIDI) calculated by using the BPCA (Figure 2). The IBB applied in this study is described as follows. The IBB simulation re-samples the observations \(X_{i}\) to \(n\) replacement (e.g., bootstrapping) by intentionally increasing or decreasing the data by as much as \(\delta_{\mu}\). The data \(X_{i}\) are increasingly ordered by assigning different weights \(W_{i,n}\) according to the magnitudes of the observations, as given below:  
\[W_{i,n}=i/n, \tag{8}\]  
where \(i=1,\,2,\,3,\,\ldots\,\,n\), and the data matrix is rearranged in the same order as the ordered \(X_{i}\). The assigned weight \(W_{i,n}\) represents the probability of selection for \(X_{i}\) data in the IBB simulation. The intentional change of increase or decrease (\(\delta_{\mu}\)) can be calculated as given in Equation (9). \[\delta_{\mu}=\widetilde{\mu}-\hat{\mu}=\frac{1}{\psi}\sum_{i=1}^{n}W_{i,n}X_{i }-\frac{1}{n}\sum_{i=1}^{n}X_{i}, \tag{9}\]  
\[\psi=\sum_{i=1}^{n}W_{i,n}. \tag{10}\]  
Figure 2: Procedure of intentionally biased bootstrap (IBB) analysis for integrated drought management.