## 1 Introduction  
In today's scientific applications, a large amount of data is generated during simulation or instrument data collection processes [1]. For example, due to the wide variety and sources of ocean data, the volume of data has grown to the scale of terabytes (TB) or even petabytes (PB), leading to a sharp increase in the costs of storage, transmission, and processing [2]. This has posed significant technological challenges for achieving fully automated analysis and traditional visualization in marine science. To effectively address this challenge, data compression algorithms have become a significant tool for reducing storage and transmission costs, improving data processing efficiency, and making it more convenient to extract and transform information from large datasets. However, pure data compression only solves part of the problem, and combining data indexing techniques with compression is expected to further improve query efficiency. Currently, data compression techniques can be broadly classified into two main types based on the degree of distortion introduced: lossless compression and lossy compression [3]. Lossless compression ensures that the decompressed data are exactly the same as the original data, either by achieving lossless compression within effective precision or by exploiting data redundancy for compression. However, the compression ratio of lossless compression is generally low, making it challenging to meet the compression needs of large datasets. On the other hand, lossy compression can be further divided into traditional lossy compression and error-bounded lossy compression. Traditional compression schemes fail to meet the precision requirements of compressed data due to their fixed compression parameters and schemes. While error-bounded lossy compression can achieve error control, the tightly coupled design in the compression and decompression processes only allows for significant compression ratios at the cost of sacrificing data precision. In practical service scenarios, data exhibit diverse spatial ranges and precision requirements. Therefore, flexible and diverse compression techniques are needed to provide efficient solutions for the storage and processing of data. Furthermore, this paper enhances the restoration of compressed data using deep learning methods. Deep learning has made significant advances in the field of image compression [4; 5; 6]. Deep neural networks, with their powerful feature extraction capabilities, have enabled the effective compression of image data without losing important visual information. However, in the field of scientific data compression, despite the enormous theoretical potential of deep learning, its actual application is relatively limited. Nevertheless, there are many deep learning methods used for data reconstruction. Autoencoders, in particular, have received great attention due to their ability to learn data representations [7]. There are currently many variants of autoencoders aimed at improving the quality of reconstructed data [1; 8; 9]. Therefore, using deep learning techniques for post-processing in data compression has become a focus of our research. This paper proposes a lossy compression technique based on error control. We first use the JPEG compression algorithm for data compression, achieving multi-level compression through continuous downsampling and setting the quality value in JPEG compression. For compressed data with different ranges and errors, we design a quadtree index structure for management. In addition, for the data restoration enhancement module, we use the ConvNeX network structure and train it with ocean data from the past five years to learn data features. This helps overcome the limitations of the JPEG compression scheme and further enhances the restoration effect. For the quadtree index structure, we also provide a range query processing algorithm to improve data query efficiency.