AACA-D-21-00020

Two datasets were used to verify the idea of this paper as shown in Figure 3. The 3D vector field data is the wind data set in MATLAB, which is the wind field data over America with data size 35x41x15 (longitude-latitude-elevation). The 2D vector field data used in this experiment are the global average monthly wind field data published by the National Oceanic and Atmospheric Administration for the period 1871-2012. The data is organized into temporal and spatial data (longitude-latitude-elevation-time), the data size is 180x91x24x1704. The bottom section (elevation 0) of the wind field in May 1873 is selected as the two-dimensional vector field data with size 180x91.To simulate different levels of data security, here we used three perturbation schemes and four rotation angle schemes. The rotation axis is set to stationary to make the results comparable. The three perturbation vector schemes are (0.1σ,0.3σ), (0.3σ,0.5σ) and (0.5σ,0.7σ); the four rotation angle schemes are (4,6), (9,11), (24,26) and (44,46). The results were saved as out-2D/3D-perturbation scheme ID-angle scheme ID (ID starting from 0). For example, out-3D1-2 means the declassification result of 3D wind field with perturbation vector scheme (0.3σ,0.5σ) and angle scheme (24,26).