Objectives  Most of the characteristics of land subsidence are analyzed separately from the perspective of temporal or spatial, and the hidden information and possible laws in the data cannot be discov‍ered simultaneously. Temporal principal component analysis (TPCA) can be used to extract temporal and spatial characteristics of temporal and spatial data in the field of geosciences. The land subsidence in the Beijing plain has typical temporal and spatial characteristics.

  Methods  (1) Permanent scatterer interferometric synthetic aperture radartechnique provide a convenient method to measure land subsidence in sub-centimeter precision. 51 Envisat ASAR data acquired from 2003 to 2010 in the Beijing plain were used to produce 50 interferograms and obtain time-series deformation with nonlinear model.(2)Based on the land subsid‍ence of about 100 000 permanent scatterer (PS) points and 51-time series, we construct the original data matrix X_{100 000×51}, calculate the correlation coefficient matrix, and use the TPCA method to analyze the temporal and spatial evolution characteristics of land subsidence in the Beijing plain.

  Results  It is found that: (1) The first principal component obtained by TPCA analysis represents the long-term development trend of the spatial distribution of land subsidence. (2) The area that the second principal component that is positive has a correlation in spatial distribution with the area of compressible layer thickness above 130 m. (3) ‍The PS points where the first principal component scores are negative and the second principal component scores are positive are distributed in the severe subsidence area above 30 mm/a. There is an obvious classification of land subsidence and seasonal variation between north and south area in the severe subsid‍ence area. Specifically, in the northern subsidence area, the amount of subsidence in spring and summer is larger than that of in autumn and winter, it is an opposite variation in the southern subsidence area.

  Conclusions  In general, the temporal and spatial variation of land subsidence could be studied for urban safety monitor‍ing by TPCA. It also can identify the main characteristics of the space and the law of temporal and spatial evolution. Since TPCA is a linear combination, by finding the direction with the largest variance for projection, the variables obtained are just uncorrelated and not independent of each other. Principal component analysis(PCA) only uses the second‍-‍order statistical information of the original data and ignores its high‍-‍order statistical information. Therefore, it is necessary to optimize by rotating principal components to find more physical meanings of principal components.