Sea Surface Temperature Reconstruction Method Based on Schatten-p Norm Constraint

Abstract Sea Surface Temperature (SST) is a core parameter that characterizes ocean-atmosphere interactions and drives the global climate system. However, limited by observational technologies, SST data generally suffers from severe missing data issues. Among traditional methods, interpolation method exhibits poor performance at high missing rates, while low-rank reconstruction based on the nuclear norm applies uniform shrinkage to singular values, leading to the loss of key information. To this end, this paper proposes an SST reconstruction method constrained by the Schatten-p norm.First, the low-rank property of the SST matrix is verified via Singular Value Decomposition (SVD), confirming that SST data can be represented by a small number of high-contribution singular values. Second, Truncated SVD is adopted to reduce the computational complexity of high-dimensional SST matrices, and the Alternating Direction Method of Multipliers (ADMM) is used to decompose the complex optimization problem constrained by the Schatten-p norm into efficiently solvable subproblems. Among these steps, the Schatten-p norm applies non-uniform penalties to singular values, which conforms to the distribution characteristics of SST data—the global structure is dominated by a few large singular values, and local details are characterized by small singular values. Finally, experiments are conducted using SST data of the South China Sea provided by the Global Argo Data Center (GDAC). Under the Missing Completely at Random (MCAR) scenario, the proposed method is compared with the traditional low-rank reconstruction method and the k-nearest neighbor interpolation method. The results show that the proposed method outperforms the comparison methods at all sampling rates. By leveraging the physical characteristics of SST data, this method effectively balances reconstruction accuracy and efficiency.