## 3 Results and Discussion  
### Three-Dimensional Modeling of the Ionosphere  
In order to verify the applicability of the spatial grid of the Earth system for spatial data, the ionosphere is an important part of the near-Earth space environment. According to the IEEE standard, the ionosphere is defined as the entire space from an altitude of 60 km above the ground to the magnetopause. Affected by solar radiation, all molecules in this layer of space are ionized and mainly exist in the form of electrons or ions, which has an important impact on the propagation of electromagnetic waves, especially in fields such as satellite navigation, radio communication, space environment prediction, and spacecraft design (ISO 2009) [34]. The IRI (International Reference Ionosphere) ionosphere model is a global empirical ionosphere model established under the leadership of the Committee on  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Composition of the Layer Body** & **Code Element of the Layer Body** & **Data Type** \\ \hline Subdivision identification of the layer body & Code of the layer-surface unit & String \\ \hline \multirow{2}{*}{Subdivision layer body} & Code of the subdivision level of & String \\  & the layer radius & String \\ \multirow{2}{*}{Code of the layer-radius unit} & Code of the layer-radius unit & String \\ \hline \hline \end{tabular}
\end{table}
Table 4: Encoding structure of the layer body.  
Space Research (COSPAR) and the International Union of Radio Science (URSI) through long-term data observation. For any given time and spatial point, this model can provide parameters such as the global-monthly-average electron density, electron temperature, and ion temperature directly within the altitude range from 50 km to 2000 km (NASA) [35]. Electron density (Ne), that is, the number of free electrons per unit volume, is a very important parameter for describing the state of the ionosphere. It varies with changes in altitude, atmospheric composition, atmospheric density, and solar radiation flux, etc.  
The data source of this study is the Global Navigation Satellite System--Total Electron Content (GNSS-TEC) database. These data contain GNSS observation data in the Receiver Independent Exchange (RINEX) format obtained from many regional GNSS receiver networks around the world. The dataset can be directly downloaded from [[https://stdb2.iese.nagoya-u.ac.jp/GPS/GPS-TEC/](https://stdb2.iese.nagoya-u.ac.jp/GPS/GPS-TEC/)]([https://stdb2.iese.nagoya-u.ac.jp/GPS/GPS-TEC/](https://stdb2.iese.nagoya-u.ac.jp/GPS/GPS-TEC/)) (accessed on 11 March 2024). This precision aids satellite navigation by resolving vertical gradients missed by 2D grids, critical for GNSS accuracy. Software tools include Python 3.10 with NumPy for grid computation and ArcGIS Pro 3.0.1 for visualization. Steps: (1) Define reference layer surfaces; (2) apply ISEA4H subdivision; (3) implement radial splitting; (4) encode using OHQS v1. The experiment was conducted on a desktop (hardware environment: Intel Core i5-6500 [EMAIL_ADDRESS] GHz, 16.0 GB RAM (Intel Corporation, Santa Clara, CA, USA), operating system: Windows 7).  
The modeling results of this type of data in the grid of the Earth-system layers are shown in Figure 16.  
In order to compare the retrieval efficiency of ISEA4H-ESSG with that of NetCDF (longitude and latitude grid) and H3 grid, 10,000 codes are randomly selected from the 5 th floor to the 12 th floor for neighborhood retrieval, and the retrieval time is tested. The comparative experiment was conducted on a desktop (hardware environment: Intel  
Figure 16: A depiction of the hierarchical data of the ionospheric electron density TEC, with the data selected on 6 February 2023.  
Core i5-6500 [EMAIL_ADDRESS] GHZ, 16.0 GB RAM, operating system: Windows 7). As shown in Figure 17, the retrieval efficiency of ISEA4H-ESSG is much higher than that of other commonly used grids.