The Geoid, Gravity and Heights - Revision Notes
This chapter is a cornerstone of geodesy and a frequent source of board-exam questions. Three distinct surfaces — the mathematical ellipsoid, the gravity-defined geoid, and the physical terrain — underlie every height measurement in geodetic engineering. The fundamental relationship h = H + N (ellipsoidal height = orthometric height + geoid undulation) is the bridge between GNSS-derived positions and the practical 'elevations above mean sea level' that engineers, planners, and surveyors use daily. In the Philippine context, GNSS surveys referenced to WGS84/PRS92 yield ellipsoidal heights, but construction projects, flood-risk mapping, and cadastral work under PD 1529 and CA 141 require orthometric heights — making geoid knowledge indispensable for every practicing Geodetic Engineer.
The Three Surfaces of Geodesy
Exam tips
- Memorise: Ellipsoid → GNSS → mathematical. Geoid → levelling → physical/gravity. Terrain → where you stand.
- Board questions often show a cross-section diagram and ask you to identify which surface is which — the geoid always undulates gently, the ellipsoid is smooth, the terrain is jagged.
- Remember that PRS92 (Clark 1866 ellipsoid) is used for horizontal control; the vertical datum in the Philippines is PVD95, tied to the geoid via mean sea level observations.
Key points
- The ELLIPSOID is a smooth, mathematically defined oblate spheroid (e.g., WGS84, GRS80, PRS92 Clarke 1866). It has no physical meaning but enables precise coordinates.
- The GEOID is the equipotential surface of the Earth's gravity field that best fits global mean sea level. It is lumpy and undulates ±100 m relative to the ellipsoid due to density variations in the Earth's crust and mantle.
- The TERRAIN (physical surface) is where measurements are actually made — always above the geoid in land surveys.
- The geoid is the reference for ORTHOMETRIC HEIGHTS (elevations 'above mean sea level'). Levelling instruments measure orthometric heights directly.
- The ellipsoid is the reference for ELLIPSOIDAL HEIGHTS, which GNSS receivers output directly.
- In the Philippines, PRS92 uses the Clarke 1866 ellipsoid. For most practical work, WGS84 and PRS92 are treated as equivalent at the metre level.
- The local mean sea level datum in the Philippines is the Philippine Vertical Datum (PVD95), derived from tide gauge observations.
Definitions
Ellipsoid
A mathematically defined oblate spheroid approximating the shape of the Earth, used as the reference surface for horizontal coordinates and ellipsoidal heights. WGS84: a = 6,378,137.0 m; f = 1/298.257223563.
Importance
Provides the geometric framework for GNSS positioning (WGS84) and the Philippine Reference System of 1992 (PRS92).
Geoid
The equipotential surface of the Earth's gravity field that closely approximates global mean sea level. Water at rest conforms to the geoid; it is not smooth but undulates due to subsurface mass irregularities.
Importance
The geoid is the physical reference for orthometric (levelled) heights — the 'elevations' used in all engineering design and legal land descriptions.
Geoid Undulation (N)
The vertical separation between the geoid and the ellipsoid at a given point. N > 0 when the geoid is above the ellipsoid; N < 0 when the geoid is below the ellipsoid.
Importance
N is the conversion factor between GNSS ellipsoidal heights and engineering orthometric heights. Values in the Philippines range approximately from +10 m to +30 m.
Orthometric Height (H)
The height of a point above the geoid, measured along the plumb line (direction of gravity). This is the 'elevation' in engineering practice, determined by spirit levelling.
Importance
Used in all cadastral, engineering, and construction surveys; the legal and practical definition of 'height above mean sea level' under PD 1529.
Ellipsoidal Height (h)
The height of a point above the ellipsoid surface, measured along the normal to the ellipsoid. Directly output by GNSS receivers.
Importance
Must be converted to orthometric height using a geoid model before use in engineering or legal contexts.
Common mistakes
- Treating GNSS ellipsoidal height as 'elevation above sea level' — these are numerically different whenever N ≠ 0.
- Confusing the geoid with mean sea level — they are approximately coincident globally but can differ locally by ±1–2 m.
- Assuming the three surfaces (ellipsoid, geoid, terrain) are always in the same vertical order — in deep ocean trenches, terrain is below the geoid.
The Fundamental Height Relationship: h = H + N
Formulas
h = H + N
Example
A GNSS survey in Metro Manila gives h = 52.30 m. The geoid model (EGM2008) gives N = −30.10 m at that point. Find H. Solution: H = h − N = 52.30 − (−30.10) = 52.30 + 30.10 = 82.40 m above mean sea level.
Variables
h = ellipsoidal height (m), H = orthometric height (m), N = geoid undulation (m). Sign convention: N > 0 when geoid is above ellipsoid.
Application
Converts between GNSS-derived ellipsoidal heights and levelled orthometric heights. Essential for all GNSS-to-elevation conversions in engineering surveys.
N = h − H
Example
A BM near Quezon City has a levelled height H = 112.20 m and a GNSS height h = 124.50 m. Find N. Solution: N = 124.50 − 112.20 = +12.30 m (geoid is 12.30 m above the ellipsoid at this point).
Variables
N = geoid undulation (m), h = ellipsoidal height from GNSS (m), H = orthometric height from spirit levelling (m).
Application
Used to derive local geoid undulation values by observing GNSS at benchmarks with known orthometric heights — the basis of gravimetric geoid modelling campaigns.
H = h − N
Example
A construction control point has h = 215.6 m and N = −28.4 m. Find H. Solution: H = 215.6 − (−28.4) = 215.6 + 28.4 = 244.0 m above mean sea level.
Variables
H = orthometric height (m), h = ellipsoidal height (m), N = geoid undulation (m).
Application
The most direct conversion used in field practice: given GNSS output (h) and a geoid model (N), compute the engineering elevation (H).
Exam tips
- Board exams almost always give two of the three values (h, H, N) and ask for the third. Isolate the unknown algebraically from h = H + N.
- Watch the sign of N in the problem statement. If 'the geoid is 30 m below the ellipsoid,' then N = −30 m.
- A quick sanity check: in the Philippines, N is typically positive (+10 to +30 m), so ellipsoidal heights h from GNSS are typically 10–30 m LESS than orthometric heights H. If your answer gives H < h by a large margin in a Philippine context, re-check the sign of N.
- For exercise 1 in the reference: h = 215.6 m, N = −28.4 m → H = 215.6 − (−28.4) = 244.0 m. For exercise 2: H = 5.0 m, h = 47.2 m → N = 47.2 − 5.0 = 42.2 m.
Key points
- The three-height relationship h = H + N is the most important formula in this chapter.
- Rearranged: H = h − N (orthometric = ellipsoidal minus undulation) and N = h − H (undulation = ellipsoidal minus orthometric).
- GNSS gives h; spirit levelling gives H; a geoid model gives N. Knowing any two, you can compute the third.
- In the Philippines, a national geoid model (EGM96, EGM2008, or PHGEOID) provides N values at any geographic coordinate.
- A negative N means the geoid is BELOW the ellipsoid — this makes H > h (the orthometric height is larger than the ellipsoidal height).
- A positive N means the geoid is ABOVE the ellipsoid — this makes H < h.
- Board Exam Rule: Always check the sign of N carefully before computing H.
Definitions
Geopotential Number (C)
The difference in gravitational potential between the geoid and the point of interest: C = W₀ − Wp (units: m²/s² or GPU). It is the rigorous basis for orthometric and dynamic heights in precise levelling.
Importance
Geopotential numbers are path-independent (unlike raw levelled differences) and are used in national precise levelling networks. On board exams, they appear in questions about dynamic heights vs. orthometric heights.
Dynamic Height (HD)
Height derived by dividing the geopotential number C by a reference gravity value γ₀: HD = C/γ₀. Unlike orthometric height, it is a purely mathematical construct not tied to the plumb line.
Importance
Used in precise levelling network adjustments where orthometric corrections are significant (e.g., high-altitude control networks).
Normal Height (HN)
Height computed using mean normal gravity along the normal plumb line from the ellipsoid to the telluroid. Used in some European and Russian vertical datums.
Importance
Distinguishes the Molodensky approach (no assumption about density below the terrain) from the Helmert orthometric approach. May appear in advanced board exam questions.
Common mistakes
- SIGN ERROR on N: H = h − N, so if N is negative (geoid below ellipsoid), subtracting a negative ADDS to h. Students often forget the double negative.
- Writing H = h + N instead of H = h − N — memorise the correct arrangement by noting 'h is at the top of the formula because the ellipsoid is at the bottom of the stack (below the geoid in many places)'.
- Using the formula without a geoid model — you cannot convert h to H from GNSS alone; a model of N is mandatory.
- Confusing orthometric and dynamic heights in levelling network problems — they differ by the orthometric correction, which depends on gravity and latitude.
Gravity: Variation, Measurement, and Role in Height Systems
Formulas
g_φ = 9.7803267715 × (1 + 0.0052790414 sin²φ + 0.0000232718 sin⁴φ) m/s²
Example
At φ = 14.6° N (Manila), sin²φ ≈ 0.0637. g_φ ≈ 9.7803267715 × (1 + 0.005279 × 0.0637) ≈ 9.7803 × 1.000336 ≈ 9.7836 m/s².
Variables
g_φ = normal gravity at geodetic latitude φ on the GRS80 ellipsoid surface. This is the Somigliana closed-form formula.
Application
Reference formula for theoretical (normal) gravity at any latitude. Used to compute gravity anomalies by comparing observed g with g_φ.
Free-Air Correction (FAC) = +0.3086 h mGal
Example
A gravity station at h = 500 m. FAC = 0.3086 × 500 = 154.3 mGal. This amount is added to observed g to compute free-air anomaly.
Variables
h = height of observation point above the ellipsoid (m). FAC is added to observed gravity when reducing to the ellipsoid/geoid level.
Application
Corrects observed gravity for the elevation of the station. A station 100 m above the geoid has observed gravity reduced by about 30.86 mGal compared to a sea-level station.
Bouguer Correction (BC) = 2πGρh = 0.04193 ρ h mGal
Example
At h = 500 m, ρ = 2670 kg/m³: BC = 0.1119 × 500 = 55.95 mGal. Bouguer anomaly = Free-air anomaly − BC.
Variables
G = gravitational constant, ρ = rock density (kg/m³, typically 2670 kg/m³ for average crustal rock), h = height (m). With ρ = 2670: BC ≈ 0.1119 h mGal.
Application
Removes the effect of the rock mass (Bouguer plate) between the station and the geoid. Always subtracted from free-air gravity.
Exam tips
- Gravity unit conversions to memorise: 1 Gal = 0.01 m/s²; 1 mGal = 10⁻⁵ m/s²; 1 μGal = 10⁻⁸ m/s². Board exams sometimes give g in Gals.
- The sequence of gravity reductions: Observed g → apply FAC → Free-Air Anomaly → subtract BC → Bouguer Anomaly. Keep the order straight.
- For board questions on gravity variation with latitude: g increases from equator to poles due to (1) shorter distance to Earth's centre at poles and (2) reduced centrifugal effect.
- Geoid modelling uses Stokes' integral with gravity anomalies — you do NOT need to compute the integral on the board exam, but you must know the input data required.
Key points
- Gravity g is the combined effect of gravitational attraction (Newton) and the centrifugal acceleration due to Earth's rotation.
- Standard gravity at the equator ≈ 9.7803 m/s²; at the poles ≈ 9.8322 m/s². The difference (~0.5%) is due to shape (polar flattening) and rotational effect.
- Gravity decreases with elevation (free-air effect): approximately −0.3086 mGal per metre of height gain (1 mGal = 10⁻⁵ m/s²).
- The FREE-AIR CORRECTION accounts for height above the ellipsoid/geoid. It is always applied before Bouguer reduction.
- The BOUGUER CORRECTION removes the gravitational effect of the rock mass between the observation point and the geoid (the Bouguer slab).
- GRAVITY ANOMALIES (free-air and Bouguer) reflect subsurface density variations and are the data input for geoid modelling via Stokes' integral.
- The geoid is defined as the surface where gravity potential W equals a constant W₀ — this is why water flows away from high-potential areas (downhill in common sense).
- Gravity is measured in the field using gravimeters (relative) or absolute free-fall instruments. Relative gravimeters measure Δg between stations.
Definitions
Free-Air Anomaly
The difference between observed gravity (corrected for elevation only, not for intervening mass) and theoretical normal gravity at the same point: Δg_FA = g_obs + FAC − g_φ.
Importance
Positive free-air anomalies indicate mass excess below; used directly in geoid determination via Stokes' formula.
Bouguer Anomaly
The free-air anomaly minus the Bouguer correction (effect of the rock slab between terrain and geoid): Δg_B = Δg_FA − BC. Reflects deep crustal density variations.
Importance
Used in geological interpretation and regional geoid modelling. Board questions may ask you to sequence the reductions (observed → free-air → Bouguer).
Equipotential Surface
A surface on which the gravity potential W is constant. The geoid is the equipotential surface W = W₀ (mean sea level). There are infinitely many equipotential surfaces; they are everywhere perpendicular to the plumb line.
Importance
Defines why water seeks the lowest potential — it flows along equipotential surfaces. Level surfaces in surveying are equipotential surfaces.
Plumb Line
The curved line everywhere tangent to the gravity vector. The direction a plumb bob hangs. Orthometric heights are measured along the plumb line from the geoid to the point.
Importance
In precise levelling, the curvature of the plumb line introduces corrections to raw height differences, especially in mountainous terrain.
Common mistakes
- Applying the free-air correction with the wrong sign — FAC is ADDED to observed gravity when reducing upward stations to the geoid.
- Using density ρ = 1000 kg/m³ (water) instead of ρ = 2670 kg/m³ (average crustal rock) in Bouguer reduction.
- Confusing 'gravity decreases with height' (true: less mass below you) with 'gravity is zero in orbit' (gravity still acts; you are in free fall).
- Forgetting that gravity anomalies — not gravity itself — are the data used to compute geoid undulations via Stokes' integral.
Practical GNSS Height Conversion and Philippine Applications
Formulas
N_interpolated ≈ N₁ + (N₂ − N₁) × d₁/(d₁ + d₂)
Example
BM-A (N = +12.5 m) is 2 km from point P; BM-B (N = +13.1 m) is 3 km from point P. N_P ≈ 12.5 + (13.1 − 12.5) × 2/5 = 12.5 + 0.24 = 12.74 m.
Variables
N₁, N₂ = geoid undulations at two known benchmarks; d₁, d₂ = distances from the unknown point to BM₁ and BM₂ respectively.
Application
Simple linear interpolation of geoid undulation between two benchmarks when a formal geoid grid is not available. Used in practical field surveys.
Exam tips
- Board exam questions on Philippine context: know that NAMRIA establishes benchmarks, PVD95 is the vertical datum, and PRS92 is the horizontal datum.
- RA 8560 is the Geodetic Engineering Act — it defines who may legally conduct surveys. PD 1529 is the Property Registration Decree — it governs how survey results are used for land titling.
- CA 141 (Public Land Act) is relevant when surveys involve public lands — know that these require DENR approval and surveys by licensed Geodetic Engineers.
- If a board question asks 'What datum is used for orthometric heights in the Philippines?' — answer: Philippine Vertical Datum 1995 (PVD95).
Key points
- In Philippine GNSS surveys (PRS92 / WGS84), all receivers output ellipsoidal height h. Engineering drawings require orthometric height H.
- The conversion H = h − N requires a geoid model. Globally, EGM96 and EGM2008 (NGS) are commonly used. The Philippines has a national geoid model available from NAMRIA.
- NAMRIA (National Mapping and Resource Information Authority) is the agency responsible for the national geodetic network, benchmarks, and vertical datum in the Philippines.
- Benchmarks (BMs) established by NAMRIA have known orthometric heights H referenced to PVD95 (Philippine Vertical Datum 1995), tied to mean sea level as observed at the Manila tide gauge.
- In GNSS surveys, you can determine N at a known BM by measuring h with GNSS and using N = h − H. These 'point undulations' can be interpolated for the survey area.
- Differential GNSS (DGNSS) and RTK surveys referenced to a base station on a known BM can propagate heights without a formal geoid model — but only within a limited area where N is approximately constant.
- Under RA 8560 (PRC Act for Geodetic Engineers), only registered Geodetic Engineers may conduct cadastral surveys, which require correct height determination under PD 1529 (Property Registration Decree).
- CA 141 (Public Land Act) land classification and surveys in the Philippines require legally valid surveys by licensed Geodetic Engineers using approved datums.
Definitions
Philippine Vertical Datum 1995 (PVD95)
The official vertical reference datum of the Philippines, defined by mean sea level observations at the Manila tide gauge. All NAMRIA benchmarks have orthometric heights referenced to PVD95.
Importance
The legal and technical zero reference for all orthometric heights in Philippine surveys. Any GNSS-derived height must be converted to PVD95 for legal cadastral and engineering submissions.
NAMRIA
National Mapping and Resource Information Authority — the primary government agency responsible for geodesy, cartography, and geographic information in the Philippines.
Importance
Maintains the national geodetic control network (horizontal via PRS92, vertical via PVD95), publishes geoid models, and sets standards for surveys under PD 1526 and related laws.
Benchmark (BM)
A permanent, fixed physical monument with a precisely determined orthometric height, established and maintained by NAMRIA. Used as reference points for all vertical control surveys.
Importance
Essential starting points for spirit levelling and GNSS+geoid conversions. Using an incorrect or destroyed BM is a common source of survey error.
Common mistakes
- Submitting GNSS ellipsoidal heights as 'elevations' in cadastral plans — this violates the requirement for orthometric heights under PD 1529.
- Assuming N = 0 in Philippine surveys — geoid undulations in the Philippines are significantly non-zero (typically +10 to +30 m), so this error causes large elevation errors.
- Using a geoid model from a different country or region without checking applicability to the Philippine setting.
- Confusing PRS92 (horizontal datum, Clark 1866 ellipsoid) with PVD95 (vertical datum, geoid-based) — these are separate reference systems.
Connections
- GNSS/GPS SURVEYING: All GNSS position outputs include ellipsoidal height h. Converting h to engineering elevation H requires a geoid model — this chapter provides the theoretical basis for that conversion, central to modern cadastral and engineering surveys in the Philippines.
- SPIRIT LEVELLING AND VERTICAL CONTROL: Levelling instruments measure orthometric height differences directly. Understanding why levelled heights are orthometric (following equipotential surfaces) is rooted in the gravity and geoid concepts in this chapter.
- MAP PROJECTIONS (PPCS/UTM): Philippine plane coordinates are computed on the PRS92 ellipsoid. Heights on Philippine maps are orthometric. The chapter explains why horizontal (ellipsoidal) and vertical (geoidal) datums are distinct systems.
- GRAVITY SURVEYING: Gravity measurements, reductions (free-air, Bouguer), and anomalies are the data source for geoid models. The gravity section of this chapter bridges geodesy and applied geophysics.
- ENGINEERING SURVEYS AND PD 1529: Legal cadastral plans and subdivision surveys submitted for land titling must use PVD95-referenced orthometric heights. The h = H + N relationship is the legal-technical bridge between GNSS technology and PD 1529 compliance.
- RA 8560 (GEODETIC ENGINEERING ACT): Defines the professional scope of Geodetic Engineers, which includes all survey work requiring correct height determination — directly dependent on geoid knowledge.
- TIDAL DATUMS AND COASTAL MAPPING: Mean sea level (approximately the geoid) is the baseline for tidal datums, flood-hazard mapping, and coastal zone management — all of which require accurate geoid knowledge.
- ADJUSTMENT OF OBSERVATIONS: Levelling network adjustments using geopotential numbers (instead of raw height differences) are conceptually linked to this chapter's discussion of dynamic and orthometric heights.
Quick review questions
A GNSS receiver outputs h = 52.30 m at a control point in Cebu. The geoid model gives N = −30.10 m. What is the orthometric height H?
Answer
H = 82.40 m above mean sea level.
Apply H = h − N = 52.30 − (−30.10) = 52.30 + 30.10 = 82.40 m. The negative N means the geoid is below the ellipsoid, so the orthometric height is larger than the ellipsoidal height. Always check the sign of N.
A benchmark near Baguio City has an orthometric height H = 112.20 m and a GNSS ellipsoidal height h = 124.50 m. What is the geoid undulation N at this point?
Answer
N = +12.30 m.
N = h − H = 124.50 − 112.20 = 12.30 m. The positive sign means the geoid is 12.30 m above the ellipsoid at this location. This is a typical positive undulation value in the Philippines.
A GNSS survey gives h = 215.6 m and the geoid model gives N = −28.4 m. Find the orthometric height H.
Answer
H = 244.0 m.
H = h − N = 215.6 − (−28.4) = 215.6 + 28.4 = 244.0 m. This is Exercise 1 from the reference material. The large difference between h and H is due to the negative (large magnitude) geoid undulation.
Given H = 5.0 m and h = 47.2 m, find the geoid undulation N.
Answer
N = +42.2 m.
N = h − H = 47.2 − 5.0 = 42.2 m. This represents a location where the geoid is 42.2 m above the ellipsoid. Despite being barely above sea level (H = 5 m), the GNSS gives h = 47.2 m because the ellipsoid is far below the geoid there.
Why does a GNSS receiver at sea level give an ellipsoidal height of approximately 40 m instead of 0 m?
Answer
Because the geoid (≈ sea level) is approximately 40 m above the ellipsoid (N ≈ +40 m) at that location.
GNSS gives h (ellipsoidal height), not H (orthometric height). At sea level, H ≈ 0, so h = H + N ≈ 0 + 40 = 40 m. The ellipsoid is 40 m below mean sea level there. Without a geoid model, GNSS heights cannot be interpreted as elevations.
In which direction does gravity act relative to an equipotential surface?
Answer
Gravity acts perpendicular to (normal to) the equipotential surface, pointing in the direction of decreasing potential.
By definition, on an equipotential surface, no work is done by gravity when moving along it. The gravity vector is therefore always normal to equipotential surfaces — this is why level surfaces in surveying (water surfaces at rest) are equipotential surfaces.
What is the approximate free-air correction rate, and in which direction is it applied when reducing observed gravity to the geoid?
Answer
Approximately +0.3086 mGal per metre of height; added to observed gravity (gravity increases as you descend toward the geoid).
Gravity decreases with height at ~0.3086 mGal/m. To 'reduce' an observation at height h back to sea level, you ADD 0.3086h mGal to the observed value. This corrects for the height difference only, without accounting for intervening mass (that is the Bouguer correction's role).
What Philippine government agency maintains the national benchmark network and provides the official geoid model?
Answer
NAMRIA (National Mapping and Resource Information Authority).
NAMRIA administers the Philippine Reference System of 1992 (PRS92) for horizontal control and PVD95 for vertical control. It maintains the benchmark network and provides geoid data. Under RA 8560, surveys must conform to NAMRIA-approved standards.
Define the geopotential number C and state its formula.
Answer
C = W₀ − Wp, where W₀ is the gravity potential at the geoid and Wp is the gravity potential at point P. Units: m²/s² or GPU (geopotential units).
The geopotential number C is the potential difference between the geoid and the point of interest. It is path-independent (unlike raw levelled height differences) and forms the rigorous basis for orthometric and dynamic heights. Dynamic height: HD = C/γ₀; Orthometric height: H = C/ḡ, where ḡ is mean gravity along the plumb line.
State the relationship between the three height types in one equation and name each variable.
Answer
h = H + N, where h = ellipsoidal height (GNSS), H = orthometric height (levelling, above geoid), N = geoid undulation (geoid above ellipsoid).
This is the master equation of the chapter. Rearrangements: H = h − N (field use: convert GNSS to elevation) and N = h − H (geoid determination: compare GNSS with levelled BM). All three surfaces are related through this single equation.
Diagrams
Chapter Mind Map: The Geoid, Gravity and Heights
A comprehensive mind map showing all major topics in this chapter and how they interconnect: the three surfaces, three height types, the master formula h = H + N, gravity concepts, and the Philippine regulatory and institutional context.
GNSS Height to Orthometric Height Conversion Procedure
A decision flowchart showing the step-by-step procedure for converting a GNSS ellipsoidal height h to an engineering orthometric height H. It covers both the direct geoid-model route and the benchmark interpolation route, with a critical sign-check step and Philippine regulatory compliance at the end.
Gravity Reduction Sequence: From Observed to Anomaly
A flowchart illustrating the sequential gravity reduction process from raw field observation to free-air and Bouguer anomalies. Shows when each correction is applied and how anomalies are used for geoid modelling (Stokes integral) versus geological interpretation.
The Three Surfaces and Height Relationships
A state diagram representing the vertical stack of the three geodetic surfaces (ellipsoid → geoid → terrain) and labelling what each separation represents: N (geoid undulation) between ellipsoid and geoid, and H (orthometric height) between geoid and terrain. The total h is the sum.
Sources of Geoid Undulation Variation
A pie chart showing the approximate relative contributions of different physical factors to geoid undulation variations globally. Crustal and mantle density anomalies dominate, explaining why the geoid undulates ±100 m relative to the smooth ellipsoid.
Evolution of Height Systems and Geodetic Datums in the Philippines
A timeline showing the historical development of Philippine geodetic datums, vertical control, and relevant legislation from the American colonial period to the present. Contextualises how the current PRS92/PVD95 system and the laws governing survey practice evolved.
Exam strategy
For the PRC Geodetic Engineer Board Examination, approach this chapter with a three-tier strategy. TIER 1 — Master the formula h = H + N and all its rearrangements. Expect at least one direct computation question: given two of the three values, find the third. Watch sign conventions — a negative N is the most common trap. TIER 2 — Know the definitions and distinctions: ellipsoidal vs. orthometric vs. dynamic height; geoid vs. ellipsoid vs. terrain; free-air vs. Bouguer anomaly. These distinctions appear in multiple-choice identification questions. TIER 3 — Understand the Philippine institutional context: NAMRIA, PVD95, PRS92, and the relevant laws (RA 8560, PD 1529, CA 141). At least one question per examination typically tests regulatory knowledge. Time management: height conversion computations should take under 2 minutes; use the formula directly. Definition and institutional questions should be answerable in 30 seconds. Prioritize Tier 1 and Tier 2 items as they carry the most weight. For checking your answers: verify that orthometric heights in the Philippines are typically 10–30 m greater than ellipsoidal heights (because N is commonly positive in the Philippine archipelago).