## 4 Experimentation and Results
### Case Study of Using Quadtree in Data Analysis  
To validate the effectiveness of the hybrid compression scheme, this study presents a case study of a typical data analysis scenario. In the field of ocean science, mesoscale eddies play a significant role in global energy and material transport due to their vertical structure and strong kinetic energy, contributing greatly to the distribution of nutrients and phytoplankton and promoting the development of marine ecosystems. However, the increase in spatial resolution in ocean numerical models and remote sensing observations has led to an increase in the available amount of ocean data, placing higher demands on the computational capabilities of automatic eddy detection algorithms. Therefore, this study compresses ocean data and then uses an eddy detection algorithm to detect the decompressed data, and it compares the results with those of the original data. The eddy detection algorithm used in this study is the angular momentum eddy detection and tracking algorithm (AMEDA) [30], which is based on physical parameters and geometric characteristics of the velocity field for eddy detection and tracking and requires variables such as sea surface height, surface geostrophic eastward sea water velocity, and surface geostrophic northward sea water velocity. Therefore, this study uses the global ocean gridded L4 sea surface height and derived variables provided by aviso to preprocess the dataset and randomly selects a continuous oceanic area from 0-25\({}^{\circ}\) N and 100-125\({}^{\circ}\) E on a randomly chosen day from 2016 to 2020 as the test data, sets the compression ratio to 23.7, and performs eddy detection on the data before and after compression,. The detection results are shown in Figure 11, where (a) represents the results of eddy detection using the original data and (b) represents the results of detection using the data compressed and decompressed in this study. From the black circles in the figure, it can be seen that for the detection of eddies in the central region, whether they are large or small eddies, or even densely distributed eddies, the detection algorithm can accurately detect them from the data processed in this study. However, for the detection of eddies at the edge, as shown in the white circles in the figure, the detection algorithm failed to detect them accurately for the processed data. The analysis suggests that this may be because the eddy detection algorithm itself needs to calculate the angular momentum and kinetic features around the eddy, while the features extracted by the network may lead to the loss of edge features due to the size of the data, resulting in detection failure. Figure 10: Comparison of data volume for the same request scope. In order to accurately assess the subtle differences between the two eddy detection results, we used the intersection over union (IoU) metric to quantify the similarity between the two eddy contours. Since eddy shapes typically appear as polygons, accurately calculating the intersection and union of two polygonal regions is geometrically complex. To simplify this calculation process, we adopted an approximate method: by randomly sampling 1000 points within each polygon, we estimated the intersection and union of the two regions. Based on these sampling points, we could efficiently calculate the IoU value, providing a quantitative measure of similarity between the two eddy contours. Specifically, our calculation is as follows:  
\[IoU=\frac{P_{eddy1\cap eddy2}}{P_{eddy1\cup eddy2}} \tag{13}\]  
In this equation, \(P_{eddy1\cup eddy2}\) represents the number of points falling into both eddy1 and eddy2 simultaneously, and \(P_{eddy1\cup eddy2}\) represents the number of points falling into either eddy1 or eddy2. In evaluating the accuracy of the detection results, we set a clear criterion: if the intersection over union (IoU) between the detected eddy contour in the processed data and its true contour exceeds 0.7, the eddy detection is considered valid.