The Geoid, Gravity and Heights - Concept Map
Height Systems in Geodesy: Understanding the Geoid, Gravity, and Three Height Measurements
Related concepts
The Geoid
Sub concepts
- Equipotential Surface
- Mean Sea Level (MSL) Approximation
- Undulations (±100 m from ellipsoid)
- Mass-Density Variations
- Gravity-Defined Surface
Relationship to central
Defines the reference surface for orthometric heights; equipotential surface of Earth's gravity field
Gravity
Sub concepts
- Latitude Variation (9.78–9.83 m/s²)
- Free-Air Reduction
- Bouguer Reduction
- Gravity Observations
- Geopotential Numbers
Relationship to central
Physical force that defines the geoid; varies with latitude, elevation, and local mass distribution
The Three Height Systems
Sub concepts
- Ellipsoidal Height (h)
- Orthometric Height (H)
- Geoidal Height (N)
- Height Conversion Formulas
- GNSS-to-Elevation Workflow
Relationship to central
Core framework relating ellipsoid, geoid, and terrain; interconnected by fundamental equation h = H + N
Ellipsoidal Height (h)
Sub concepts
- WGS84 Reference Ellipsoid
- PRS92 (Philippine Reference System)
- GNSS Output
- Geometric Height
Relationship to central
Height above the mathematical reference ellipsoid (WGS84/PRS92); what GNSS receivers measure directly
Orthometric Height (H)
Sub concepts
- Mean Sea Level Reference
- Spirit Levelling
- Engineering Elevation
- Dynamic Height vs Orthometric
Relationship to central
Height above the geoid (MSL); practical engineering elevation obtained from spirit levelling
Geoid Undulation (N)
Sub concepts
- Sign Convention
- Geoid Models (PGM, EGM96, EGM2008)
- Regional Variation
- Computation from h and H
Relationship to central
Vertical separation between ellipsoid and geoid; negative where geoid is below ellipsoid
Fundamental Relationship: h = H + N
Sub concepts
- Rearrangement: H = h − N
- Rearrangement: N = h − H
- Sign-of-N Pitfall
- Application in Field Practice
Relationship to central
Core mathematical equation linking all three height systems; enables GNSS-to-elevation conversion
Geoid Modelling and Applications
Sub concepts
- Global Geoid Models (EGM2008, EIGEN-6C4)
- Regional Models (PGM, PRS92-based)
- Grid Interpolation
- GNSS-to-Levelling Conversion
Relationship to central
Practical tools and methods for converting ellipsoidal to orthometric heights in Philippine surveying
Common Pitfalls and Misconceptions
Sub concepts
- Confusing h and H
- Sign Error in N
- Missing Geoid Model
- Orthometric vs Dynamic Heights
Relationship to central
Critical exam and field errors that challenge understanding of height systems
Concept connections
- The GeoidOrthometric Height (H)Geoid is the reference surface; orthometric height is measured perpendicular to it along the gravity field
- GravityThe GeoidGravity field defines the geoid as an equipotential surface; variations in gravity create geoid undulations
- Ellipsoidal Height (h)Orthometric Height (H)Related through geoid undulation; h = H + N; GNSS measures h, engineering needs H
- Geoid Undulation (N)Fundamental Relationship: h = H + NN is the third component of the fundamental equation; solving for any two gives the third
- Fundamental Relationship: h = H + NGNSS to Elevation WorkflowThe equation is the mathematical basis for the entire workflow; rearranged as H = h - N
- GravityOrthometric Height (H)Orthometric height system is defined using gravity potential; geopotential numbers give rigorous heights
- Geoid Modelling and ApplicationsGNSS to Elevation WorkflowGeoid models provide the N values needed to compute H from h; essential for practical conversion
- Common Pitfalls and MisconceptionsFundamental Relationship: h = H + NMost pitfalls arise from misunderstanding the equation: sign of N, confusing h and H, or missing the model
- Ellipsoidal Height (h)Geoid Undulation (N)Both are measurements along the vertical direction; h is from GNSS, N from geoid model at same location
- GravityGeoid Modelling and ApplicationsGlobal geoid models like EGM2008 are constructed from gravity measurements and satellite data
- The Three Height SystemsFundamental Relationship: h = H + NThe three systems (h, H, N) are unified by this single mathematical equation
- Common Pitfalls and MisconceptionsSign Convention for Geoid Undulation NSign error (double negative) is the most common exam mistake; critical to understand N can be positive or negative
Diagrams
The Geoid, Gravity and Heights — Comprehensive Concept Hierarchy
Comprehensive mind map showing the hierarchical relationships among all concepts in the chapter: The Geoid, Three Height Systems, Gravity, the fundamental equation h = H + N, the GNSS-to-elevation workflow, and common misconceptions. This is the primary visual organizer for understanding how all topics interconnect.
GNSS to Orthometric Height Conversion Process
Step-by-step flowchart showing how GNSS ellipsoidal heights (h) are converted to practical orthometric heights (H) using a geoid model. Highlights the critical decision points and sign-convention checks. This is the standard workflow for Philippine surveying under PRS92.
Height System Selection and Application Matrix
Decision flowchart for selecting and applying the appropriate height system based on the surveying or engineering application. Shows how each system (ellipsoidal, orthometric, dynamic) is chosen and its advantages and limitations in Philippine practice.
Data Flow: From Field Measurement to Orthometric Height
Sequence diagram showing the data flow from GNSS measurement through geoid model lookup to final orthometric height calculation and engineering application. Shows the interaction between field instrument, computational model, and end-user.
Sign Convention for Geoid Undulation N: Critical Decision Tree
Critical decision tree for understanding the sign convention of geoid undulation N and avoiding the most common exam error: the double-negative mistake when N is negative. Shows concrete numerical examples with correct calculations.
Geoid Properties and Evolution Through Understanding
State diagram showing the logical progression from understanding the geoid as an equipotential surface through its properties, gravity linkage, mathematical modelling, and practical application in height conversion. Shows how conceptual understanding leads to field implementation.
Sources of Error in GNSS-to-Orthometric Height Conversion
Pie chart showing the approximate contribution of various error sources when converting GNSS ellipsoidal heights to orthometric heights. Emphasizes that geoid model accuracy and GNSS measurement quality dominate the uncertainty budget, with sign errors as a notable but avoidable source.