GELE Geodesy — The Geoid, Gravity and HeightsConcept Map

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

Concept

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

To

Orthometric Height (H)

From

The Geoid

Strength

strong

Relationship

Geoid is the reference surface; orthometric height is measured perpendicular to it along the gravity field

To

The Geoid

From

Gravity

Strength

strong

Relationship

Gravity field defines the geoid as an equipotential surface; variations in gravity create geoid undulations

To

Orthometric Height (H)

From

Ellipsoidal Height (h)

Strength

strong

Relationship

Related through geoid undulation; h = H + N; GNSS measures h, engineering needs H

To

Fundamental Relationship: h = H + N

From

Geoid Undulation (N)

Strength

strong

Relationship

N is the third component of the fundamental equation; solving for any two gives the third

To

GNSS to Elevation Workflow

From

Fundamental Relationship: h = H + N

Strength

strong

Relationship

The equation is the mathematical basis for the entire workflow; rearranged as H = h - N

To

Orthometric Height (H)

From

Gravity

Strength

strong

Relationship

Orthometric height system is defined using gravity potential; geopotential numbers give rigorous heights

To

GNSS to Elevation Workflow

From

Geoid Modelling and Applications

Strength

strong

Relationship

Geoid models provide the N values needed to compute H from h; essential for practical conversion

To

Fundamental Relationship: h = H + N

From

Common Pitfalls and Misconceptions

Strength

moderate

Relationship

Most pitfalls arise from misunderstanding the equation: sign of N, confusing h and H, or missing the model

To

Geoid Undulation (N)

From

Ellipsoidal Height (h)

Strength

moderate

Relationship

Both are measurements along the vertical direction; h is from GNSS, N from geoid model at same location

To

Geoid Modelling and Applications

From

Gravity

Strength

moderate

Relationship

Global geoid models like EGM2008 are constructed from gravity measurements and satellite data

To

Fundamental Relationship: h = H + N

From

The Three Height Systems

Strength

strong

Relationship

The three systems (h, H, N) are unified by this single mathematical equation

To

Sign Convention for Geoid Undulation N

From

Common Pitfalls and Misconceptions

Strength

strong

Relationship

Sign error (double negative) is the most common exam mistake; critical to understand N can be positive or negative