Time Series Analysis of Long-term Terrestrial Water Storage over Canada from GRACE Satellites Using Principal Component Analysis

Abstract. Principal component analysis (PCA) is a statistical technique widely used in remote sensing, yet few studies have addressed the physical meaning of component images. Using PCA, this study analyzed the long-term (2003–2013) monthly terrestrial water storage (TWS) over Canada time series dataset from the Gravity Recovery and Climate Experiment (GRACE) mission. The principal components were physically explained through establishing the mathematical relationship between the pixel values of a component image and the correlation coefficients between the original data and the loadings of the component image. It is found that the 1st component of the data represented the long-term TWS trend over the study period. The 2nd component represented the monthly variation of TWS. The 3rd and the 4th components reflected the spatial and temporal anomalies of TWS. The 1st component contained 49.3 % of the TWS variance. The first 4 components explained a total of 87.1 % of the data variance. The TWS changes captured by the PCA were largely contributed by the changes in precipitation over Canada. This study provides an approach for physically interpreting the principal components and their loadings in PCA.