Exploration of Earth Gravitational Models (EGM) including EGM2008, EIGEN-6C4, and satellite-only models from GRACE and GOCE missions.
\[V(r,\theta,\lambda) = \frac{GM}{r}\sum_{n=0}^{N_{max}}\left(\frac{a}{r}\right)^n\sum_{m=0}^{n}\bar{P}_{nm}(\cos\theta)[\bar{C}_{nm}\cos(m\lambda) + \bar{S}_{nm}\sin(m\lambda)]\]
High-resolution combined model incorporating satellite, airborne, and terrestrial data.
Max Degree: 2190 | Resolution: ~9 km
Release: 2008 | Agency: NGA
Combined model from GRACE, GOCE, and surface data with improved medium wavelengths.
Max Degree: 2190 | Resolution: ~9 km
Release: 2014 | Agency: GFZ/GRGS
Satellite-only model combining GRACE and GOCE observations.
Max Degree: 300 | Resolution: ~66 km
Release: 2020 | Agency: TU Graz
Monthly gravity solutions for temporal mass variations.
Max Degree: 96 | Resolution: ~200 km
Release: 2023 | Agency: CSR/GFZ/JPL
| Model | Max Degree | Data Sources | Geoid σ (cm) | Year |
|---|---|---|---|---|
| EGM2008 | 2190 | GRACE + Altimetry + Surface | 15 | 2008 |
| EIGEN-6C4 | 2190 | GRACE + GOCE + Surface | 12 | 2014 |
| GOCO06s | 300 | GRACE + GOCE | 2 (to d/o 200) | 2020 |
| XGM2019e | 5540 | Multi-source | 10 | 2019 |
\[\sigma_n^2 = \sum_{m=0}^{n}(\bar{C}_{nm}^2 + \bar{S}_{nm}^2)\]
Kaula's Rule: \(\sigma_n \approx \frac{10^{-5}}{n^2}\)
Geoid models define the reference surface for orthometric heights, enabling conversion between GPS ellipsoidal heights and practical leveling heights. Critical for engineering and construction.
Gravity field models are essential for precise orbit determination of satellites. Higher degree models improve prediction accuracy for low-Earth orbiters.
Gravity compensation in INS requires accurate local gravity knowledge. EGM models enable sub-mGal accuracy for precision navigation applications.
Mean dynamic topography (MDT) derived from altimetry minus geoid reveals ocean circulation patterns. GOCE improved MDT accuracy significantly.
Gravity anomalies reveal density variations in Earth's crust and mantle. Used for mineral exploration, geothermal studies, and understanding tectonics.
GRACE time-variable gravity tracks water mass redistribution: groundwater depletion, ice sheet mass loss, and seasonal water storage changes.
| Application | Required Accuracy | Spatial Resolution | Recommended Model |
|---|---|---|---|
| GNSS Leveling | 1-2 cm | 5-10 km | Regional + EGM2008 |
| LEO Orbit Determination | 1 cm | 100 km | GOCO06s |
| Oceanography | 1-2 cm | 100 km | EIGEN-6C4 |
| Exploration Geophysics | 1 mGal | 1-5 km | Local surveys |
| Ice Mass Balance | mm/yr water eq. | 300 km | GRACE-FO monthly |