## 1 Introduction
### Current Research Status of Earth Spatial Grid
Spheroidal spatial grid research, often framed within Earth-system science and global-scale challenges, targets medium- to ultra-large-scale phenomena such as tectonic plate movements, regional geological activities, atmospheric and oceanic circulation, ionospheric dynamics, geomagnetic fields, and near-Earth environmental interactions. Commonly used spheroidal grid systems include:  
1. Latitude-longitude spheroidal grids: Extend 2D grids radially but suffer from polar distortion [24]. 2. Cubed-sphere grids: Use cubic projections for uniform coverage, suited for atmospheric modeling [25]. 3. Yin-Yang Grid: Designed for mantle convection with overlapping domains [26]. 4. Adaptive Mesh Refinement (AMR): Dynamically adjusts resolution for localized phenomena [27]. 5. Sphere Degenerated Octree Grid (SDOG): Employs octree subdivision for 3D Earth modeling but lacks flexible layering [28]. This numbered format enhances clarity and allows readers to quickly grasp the diversity of spheroidal grids. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Grid Type** & **Structural Features** & **Representative Models** & \multicolumn{2}{c}{**Advantages and**} \\  & & & & **Limitations** & **Typical Applications** \\ \hline Triangular Grids & Based on octahedrons/icoshedrons, & QTM (Quaternary Triangular Mesh) [19] & Pros: Hierarchical continuity & \\  & hierarchical but geometrically complex & Mesh [19] & Cons: Complex neighborhood algorithms, irreducible geometric distortion & Global terrain modeling \\  & & SQT (Spheroidal Tree) [20] & & & Spatial indexing \\ Quadrilateral Grids & Merged triangular units; simplified adjacency relations & Octahedral homous subdivision & Pros: Simplified neighborhood operations & \\  & & Quadtree-extended models & Cons: Limited flexibility, minor & Hierarchical analysis \\  & & H3 (seven-aperture) & & & \\  & & rHEALPix (refined Hierarchical & Pros: Dynamic modeling & \\  & Grids & High adjacency symmetry; optimal & Equal-Area iso-latitude & \\  & & Coverage efficiency & Pielezideno) [21] & Cons: High encoding complexity, & Multi-resolution \\  & & ORGS (Optimized Hexagonal & projection approximation required & platforms \\  & & Quadtree Structured) [22] & & & \\ \hline \hline \end{tabular} Note: QTM: Quaternary Triangular Mesh; SQT: Sphere Quad Tree; H3: Uber’s open-source hexagonal grid system; rHEALPix refined Hierarchical Equal-Area Pixelization; OHQS: Optimized Hexagonal Quadtree Structure.  
\end{table} 
Table 1: Regular polyhedron-based grids. These grids exhibit domain-specific innovations tailored to distinct Earth-system applications. The evolution of Earth spatial grids has progressed from local planar grids to 3D grids, and from spherical grids to spheroidal grids. While spherical grids abstract Earth's space as a surface, suitable for representing surface-level phenomena, they fail to rigorously model 3D objects [29]. Spheroidal grids treat Earth as a homogeneous sphere with radial hierarchies, but these hierarchies cannot be flexibly adjusted--they rely on radial subdivision to approximate predefined spherical layers, inadequately capturing true layered structure. Spheroidal grids (e.g., SDOG) approximate layers radially yet struggle with flexible stratification [28]. For instance, SDOG approximates atmospheric layers but cannot flexibly adjust to the ionosphere's variable thickness [28]. ISEA4H-ESSG bridges these gaps with adaptive 3D layering. Spatial phenomena and processes interact across scales, necessitating a unified multi-scale 3D grid framework for coupled modeling. Constructing a layered and adapted 3D grid with figures requires adaptive modifications in grid design, subdivision encoding, and data models to align with Earth's layered structure. Such a framework must not only describe activities within individual layers but also unify cross-layer spatial representations, ultimately establishing an integrated spatial framework encompassing terrestrial, atmospheric, and celestial domains.