## 3 Results and Discussion
### Formatting of Mathematical Components  
Atmospheric temperature affects the motion state of the atmosphere, the formation of clouds, and precipitation. It is one of the main controlling factors for the state and evolution of the climate system. Meanwhile, it also influences the growth of organisms on the land surface, and is one of the most basic characteristic parameters of the atmosphere. The three-dimensional modeling of the global atmospheric temperature field plays an important role in studying global climate change, the ecological environment, the growth of vegetation, etc.  
The NCEP reanalysis data are released in quasi-real-time online by the National Centers for Environmental Prediction (NCEP) and the National Center for Atmospheric Research [36]. It contains data of more than 50 years. This dataset is obtained after carrying out quality control and assimilation processing on the observation data from the ground, ships, radiosondes, weather balloons, aircraft, satellites, etc. The National Centers for Environmental Prediction (NCEP) in the United States releases the global \(1^{\circ}\times 1^{\circ}\) atmospheric reanalysis data in GRIB format to the public every 6 h on average ([[https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html](https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html)]([https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html](https://psl.noaa.gov/data/gridded/data.ncep.reanalysis.html)), accessed on 11 March 2024), which includes parameter data such as air temperature, humidity, wind direction, and aerosols. The atmospheric temperature data are one of the numerous parameters in the reanalysis data, and its vertical range is from 10 hPa to 1000 hPa. This precision aids satellite navigation by resolving vertical gradients missed by 2D grids, critical for GNSS accuracy.  
This type of data includes parameters such as vertical velocity and temperature. Its resolution in the Earth's radial direction is approximately 0.1 to 0.5 km, while the resolution on the spherical surface is approximately 110 km \(\times\) 110 km (close to \(1^{\circ}\times 1^{\circ}\)).  
According to the characteristics of the NCEP FNL data, it is necessary to first carry out the subdivision of the layer radius until the ratio of the side length of the layer-radius division unit to that of the initial layer cell is close to 0.5 km:110 km (that is, 1:220).  
Figure 17: Comparison of retrieval efficiency between H3, Jingwei grid and ISEA4H-ESSG.  
Let the subdivision level of the layer radius be n, then the length of the radial side d = D/2n. When the length of the radial side is approximately equal to the length of the latitude side b of the equator in the first-level layer cell, that is  
\[d\approx b/220\]  
where  
\[b=2\pi\ R/4\times 2^{1}\approx 5009\ \text{km}\]  
Then, there is  
\[n=5\]  
Therefore, it is necessary to carry out the subdivision of the layer radius five times, and then carry out the hierarchical subdivision according to ISEA4H according to the resolution, as shown in Figure 18.  
Based on the grid-data-accuracy evaluation index system [37] proposed by [PERSON] et al., the accuracy of NCEP data before and after conversion is evaluated, and the information entropy index is 0.976, the pixel RMSE is 7.45, and the interactive information is 0.984. The data recombination accuracy is good.