# Sparse Data-Extended Fusion Method for Sea Surface Temperature Prediction on the East China Sea
## 1 Introduction  
Sea surface temperature (SST) is the basic tool for understanding local and global climate change. The study of SST changes in marginal seas under the background of global warming has always been an important topic in regional oceanography and climatology [1]. Variability of SST will cause weather phenomenon changes, such as tropical monsoons and cyclones. The inseparable connection between the variability of Indian Ocean SST and the Indian summer monsoon has long been known [2]. SST variability has a great impact on the habits of marine organisms. For instance, predicting fishing areas is based on the potential law of the SST variability [3]. Moreover, marine ecosystems are affected by SST variability. For example, due to climate warming, coral reefs have a lower growth rate in the west, and the strong positive Indian Ocean dipole mode events (IOD) also caused catastrophic damage to the coral reefs of the Mentawi Islands [4]. Therefore, predicting SST in advance can not only protect related resources, but also prevent major losses caused by certain marine disasters. SST is mainly obtained from satellite remote sensing and in situ observation including marine stations, buoys, and voluntary observing ships et al. Satellite remote sensing data has the advantages of all-weather and high spatio-temporal resolution, which has gradually become an indispensable means of marine research. However, the accuracy of satelliteremote sensing inversion is relatively low. Data from in situ observation including ocean stations, buoys [5], and volunteer ships [6] have high accuracy but sparse and uneven distribution. As a result, it is difficult to obtain the continuous, accurate and uniform SST and finally the prediction accuracy of SST is much lower in the wide range. Therefore, how to effectively integrate the in situ observational data with remote sensing data becomes a big challenge in marine environmental monitoring and prediction. Furthermore, the problems of sparse and uneven distribution of in-situ observation data and low accuracy of satellite data are also troublesome. At present, the main methods for fusing observation data and remote sensing data to become standardized grid data products include the interpolation method [7], the variational method [8], the Kalman filter method [9], and the deep learning method [10]. Among the interpolation methods, optimal interpolation (OI) is the most classic one. [PERSON] et al. [11; 12] applied OI into the fusion analysis of satellite SST with field observation data, and finally produced average SSTs of monthly, weekly, and daily. One disadvantage of the OI method is that the background error covariance matrix is static, and the advantage of the variational method over OI is that the variational method [13] introduces a nonlinear observation operator, which avoids the limitation of the linear relationship between observed quantity and analytical quantity in the OI method [14]. The variational method is a global optimization whereas OI is a local optimization. In addition, the variational method can also introduce some dynamic constraints. Variational methods mainly include three-dimensional variation (3 DVAR) and four-dimensional variation (4 DVAR). 4 DVAR is an improvement from 3 DVAR. Due to the limitations of the existing optimization algorithm, its convergence is reduced due to the introduction of mode constraints, and because of the roughness of the initial guess field, it doesn't converge to a global minimum, but converges to a local extreme value, which seriously affects the expected effect of the 4 DVAR method. The Kalman filter (KF) was originally proposed by [PERSON] [15]. Compared with the variational method, the advantage of KF is that there is no need to write the accompanying pattern, and the disadvantage is that it needs to store a high-dimensional background error covariance matrix and requires an accurate estimation of the model error. In recent years, the rapid development of artificial intelligence has brought new ideas for ocean data fusion.