1.4 Vertical datums and height systems

Vertical datums and height systems are crucial for accurately representing Earth's topography in geospatial applications. They provide consistent reference surfaces for measuring elevations, essential for mapping, engineering, and environmental analysis.

Understanding different types of vertical datums and height systems is key to integrating and analyzing geospatial data. This knowledge enables professionals to choose appropriate references for projects and perform accurate transformations between different systems.

Vertical datums

• Vertical datums provide a consistent reference surface for measuring elevations and heights
• Essential for accurately representing and analyzing the Earth's topography and features in geospatial applications
• Different types of vertical datums are used depending on the specific requirements and geographic extent of a project

Geoid as reference surface

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• The geoid serves as a fundamental reference surface for vertical datums
• Represents the equipotential surface of the Earth's gravity field that closely approximates mean sea level
• Provides a physically meaningful and globally consistent reference for measuring heights

Tidal vs orthometric datums

• Tidal datums are based on long-term observations of sea level at specific locations (tide gauges)
• Orthometric datums are based on the geoid and account for variations in the Earth's gravity field
• Tidal datums are locally defined and can vary significantly between different coastal regions
• Orthometric datums provide a more consistent and globally applicable reference for heights

Local vs global datums

• Local vertical datums are established for specific regions or countries based on local sea level observations and leveling networks
• Global vertical datums aim to provide a unified and consistent reference surface for heights worldwide
• Local datums may have offsets and biases relative to each other and to global datums
• Transitioning from local to global datums requires careful consideration of datum transformations and geoid modeling

Height systems

• Height systems define the method and reference surface used to assign elevations to points on the Earth's surface
• Different height systems have specific properties and are suited for different applications
• Understanding the differences between height systems is crucial for accurate data integration and analysis

Ellipsoidal heights

• Ellipsoidal heights are measured along the normal to the reference ellipsoid from the point of interest
• Purely geometric and do not consider the Earth's gravity field
• Can be obtained directly from GNSS measurements
• Not physically meaningful for many applications that require heights relative to a gravitational reference surface

Orthometric heights

• Orthometric heights represent the distance along the plumb line from the point of interest to the geoid
• Account for variations in the Earth's gravity field and provide physically meaningful heights
• Require knowledge of the geoid height (geoid undulation) relative to the reference ellipsoid
• Commonly used in surveying, mapping, and engineering applications

Geoid undulations

• Geoid undulations, also known as geoid heights, represent the separation between the geoid and the reference ellipsoid
• Positive when the geoid is above the ellipsoid and negative when the geoid is below the ellipsoid
• Vary spatially due to the non-uniform distribution of mass within the Earth
• Can range from -100 m to +100 m globally

Height system transformations

• Transforming heights between different height systems requires accounting for the geoid undulation
• Ellipsoidal heights can be converted to orthometric heights by subtracting the geoid undulation: $H = h - N$
  • $H$ is the orthometric height
  • $h$ is the ellipsoidal height
  • $N$ is the geoid undulation
• Accurate geoid models are essential for performing height system transformations

Gravity and the geoid

• The Earth's gravity field plays a fundamental role in defining the geoid and vertical datums
• Understanding the relationship between gravity and the geoid is essential for accurate height determination and vertical datum realization

Gravity potential

• Gravity potential is a scalar field that represents the work required to move a unit mass from infinity to a point in the Earth's gravity field
• Varies with location due to the non-uniform distribution of mass within the Earth
• Surfaces of equal gravity potential, known as equipotential surfaces, are perpendicular to the direction of gravity at every point

Equipotential surfaces

• Equipotential surfaces are surfaces on which the gravity potential is constant
• The geoid is a particular equipotential surface that closely approximates mean sea level
• Other equipotential surfaces, such as the reference ellipsoid, are used in geodetic applications
• Equipotential surfaces are not parallel to each other due to variations in the Earth's gravity field

Geoid determination methods

• Gravimetric methods: Determine the geoid using measurements of the Earth's gravity field
  • Terrestrial gravity measurements
  • Airborne and satellite gravimetry
  • Gravity field models derived from satellite observations (GRACE, GOCE)
• Geometric methods: Determine the geoid using a combination of GNSS and leveling measurements
  • GNSS/leveling: Measure ellipsoidal heights (GNSS) and orthometric heights (leveling) at common points
  • Compute geoid undulations as the difference between ellipsoidal and orthometric heights
• Combined methods: Integrate gravimetric and geometric techniques to improve geoid determination accuracy

Vertical datum realization

• Vertical datum realization involves establishing a physical reference surface that represents the vertical datum
• Requires a combination of measurements and observations to define the datum and its relationship to the Earth's gravity field

Tide gauge measurements

• Tide gauges measure sea level variations over time at specific coastal locations
• Provide a local reference for establishing tidal datums
• Long-term tide gauge records are used to determine mean sea level and other tidal datum parameters
• Tide gauge measurements are affected by factors such as ocean currents, atmospheric pressure, and vertical land motion

Leveling networks

• Leveling networks consist of a series of benchmarks connected by precise leveling measurements
• Used to establish and maintain vertical control for a region or country
• Leveling measurements determine height differences between benchmarks
• Leveling networks are referenced to a specific vertical datum, often defined by a primary tide gauge

Gravity observations

• Gravity observations are used to determine the shape of the Earth's gravity field and to define the geoid
• Terrestrial gravity measurements are collected at benchmarks and other control points
• Airborne and satellite gravimetry provide broader coverage and help refine regional and global geoid models
• Gravity observations are combined with other measurements (GNSS, leveling) to realize a vertical datum

Vertical datum unification

• Vertical datum unification aims to establish a consistent and globally referenced vertical datum
• Necessary for seamless integration and comparison of geospatial data from different regions and sources

Datum biases and offsets

• Different vertical datums may have biases and offsets relative to each other
• Biases can arise from differences in the definition, realization, and reference surface of the datums
• Offsets can occur due to factors such as sea level variations, crustal deformation, and datum drift over time
• Identifying and quantifying datum biases and offsets is crucial for vertical datum unification

Least squares adjustment

• Least squares adjustment is a mathematical technique used to estimate datum parameters and minimize residuals
• Combines measurements from different sources (GNSS, leveling, gravity) and considers their uncertainties
• Provides a statistically rigorous approach for determining datum transformations and assessing their accuracy
• Allows for the estimation of vertical datum offsets and the unification of multiple datums

Geoid modeling in unification

• Accurate geoid modeling is essential for vertical datum unification
• Geoid models provide a common reference surface for relating different vertical datums
• Regional and global geoid models are developed using a combination of gravity, GNSS, and leveling data
• Geoid models are continually refined as more data becomes available and computational techniques improve

Applications in geospatial engineering

• Vertical datums and height systems have numerous applications in geospatial engineering
• Accurate and consistent vertical information is crucial for various projects and decision-making processes

Topographic mapping

• Vertical datums provide the reference for assigning elevations to features on topographic maps
• Consistent use of vertical datums ensures compatibility and accuracy of elevation data across different map sheets and scales
• Digital Elevation Models (DEMs) and contours are derived using vertical datum information

Floodplain management

• Vertical datums are essential for delineating floodplains and assessing flood risks
• Flood elevations and inundation extents are referenced to a specific vertical datum
• Accurate vertical datum information is crucial for flood hazard mapping, insurance rating, and mitigation planning

Infrastructure design

• Vertical datums are used in the design and construction of infrastructure projects (roads, bridges, pipelines)
• Ensure that elevations and grades are consistent and compatible across the project
• Critical for drainage design, clearance requirements, and utility coordination
• Vertical datum inconsistencies can lead to construction errors and increased costs

Geodetic surveying considerations

• Choosing an appropriate vertical datum is important for geodetic surveying projects
• Consider factors such as the project location, extent, accuracy requirements, and compatibility with existing data
• Proper documentation and metadata of the vertical datum used is essential for data sharing and future reference
• Surveyors must be aware of vertical datum transformations and geoid modeling methods when working with height data from different sources