Ellipsoid and Geoid

In GIS and geodesy, the ellipsoid and geoid are fundamental models used to approximate the shape of the Earth. They serve as reference surfaces for geographic coordinate systems, positioning, and elevation measurements.

1. Ellipsoid (Spheroid)

An ellipsoid (or spheroid) is a mathematically defined smooth surface that approximates the Earth's shape. It is formed by rotating an ellipse around its minor axis, making the Earth slightly flattened at the poles and bulging at the equator.

Semi-Major Axis (a): The longest radius, measured along the equatorial plane.
Semi-Minor Axis (b): The shortest radius, measured from the center to the poles.
Flattening (f): The measure of how much the ellipsoid is compressed at the poles. Calculated as: f=a−baf = \frac{a - b}{a}
Reference Ellipsoid: A specific mathematical model used in geodetic calculations.

Examples of Ellipsoids

WGS84 (World Geodetic System 1984) – Used globally, including for GPS.
GRS80 (Geodetic Reference System 1980) – Used in North America.
Clarke 1866 – Older model used in North American mapping.

Practical Use Cases

GPS and Google Maps use the WGS84 ellipsoid for positioning.
GIS software relies on ellipsoidal coordinates to ensure accurate mapping.

2. Geoid

A geoid is a model of the Earth's shape based on gravity measurements. It represents the mean sea level (MSL) extended under landmasses, showing where gravity is constant. Unlike the smooth ellipsoid, the geoid has an irregular shape due to variations in Earth's gravity.

Geoidal Height (N): The difference between the geoid and the reference ellipsoid at any location. N=h−HN = h - H Where:
- h = Ellipsoidal height (from GPS)
- H = Orthometric height (real elevation above the geoid)
- N = Geoid undulation (difference between ellipsoid and geoid)

Examples of Geoid Models

EGM96 (Earth Gravitational Model 1996) – Used globally for precise height measurements.
EGM2008 – A more refined version for better accuracy.
NAVD88 (North American Vertical Datum 1988) – Used in the United States for elevation data.

Practical Use Cases

Flood risk mapping requires geoid-based elevations (orthometric heights).
Satellite altimetry uses geoid models to measure sea level changes.
Surveying and engineering projects use geoid corrections for precise elevation data.

3. Comparison

Feature	Ellipsoid	Geoid
Definition	A mathematically perfect surface approximating Earth's shape.	A physical model based on Earth's gravity field.
Surface Type	Smooth and regular.	Irregular, follows mean sea level.
Used For	Defining latitude, longitude, and ellipsoidal heights.	Defining mean sea level and orthometric heights.
Reference Models	WGS84, GRS80, Clarke 1866.	EGM96, EGM2008, NAVD88.
Key Application	GPS navigation, cartography.	Elevation modeling, sea level studies.

4. Importance in GIS

Accurate Positioning: GPS provides ellipsoidal height, but real-world applications require geoid-based heights.
Elevation Corrections: Engineers and surveyors use geoid models to adjust GPS height data.
Map Projections: Selecting the right reference ellipsoid ensures accurate geographic data representation.

The ellipsoid is a smooth, mathematical model used for latitude/longitude measurements.
The geoid is a gravity-based, irregular surface that represents mean sea level.
GIS applications often convert ellipsoidal heights (from GPS) to orthometric heights (using geoid models) for real-world accuracy.

Comments

geostationary and sun-synchronous

Orbital characteristics of Remote sensing satellite geostationary and sun-synchronous Orbits in Remote Sensing Orbit = the path a satellite follows around the Earth. The orbit determines what part of Earth the satellite can see , how often it revisits , and what applications it is good for . Remote sensing satellites mainly use two standard orbits : Geostationary Orbit (GEO) Sun-Synchronous Orbit (SSO) Geostationary Satellites (GEO) Characteristics Altitude : ~35,786 km above the equator. Period : 24 hours → same as Earth's rotation. Orbit type : Circular, directly above the equator . Appears "stationary" over one fixed point on Earth. Concepts & Terminologies Geosynchronous = orbit period matches Earth's rotation (24h). Geostationary = special type of geosynchronous orbit directly above equator → looks fixed. Continuous coverage : Can monitor the same area all the time. Applications Weather...

Disaster Management

1. Disaster Risk Analysis → Disaster Risk Reduction → Disaster Management Cycle Disaster Risk Analysis is the first step in managing disasters. It involves assessing potential hazards, identifying vulnerable populations, and estimating possible impacts. Once risks are identified, Disaster Risk Reduction (DRR) strategies come into play. DRR aims to reduce risk and enhance resilience through planning, infrastructure development, and policy enforcement. The Disaster Management Cycle then ensures a structured approach by dividing actions into pre-disaster, during-disaster, and post-disaster phases . Example Connection: Imagine a coastal city prone to cyclones: Risk Analysis identifies low-lying areas and weak infrastructure. Risk Reduction includes building seawalls, enforcing strict building codes, and training residents for emergency situations. The Disaster Management Cycle ensures ongoing preparedness, immediate response during a cyclone, and long-term recovery afterw...

Linear Arrays Along-Track Scanners or Pushbroom Scanners

Multispectral Imaging Using Linear Arrays (Along-Track Scanners or Pushbroom Scanners) Multispectral Imaging: As previously defined, this involves capturing images using multiple sensors that are sensitive to different wavelengths of electromagnetic radiation. Linear Array of Detectors (A): This refers to a row of discrete detectors arranged in a straight line. Each detector is responsible for measuring the radiation within a specific wavelength band. Focal Plane (B): This is the plane where the image is formed by the lens system. It is the location where the detectors are placed to capture the focused image. Formed by Lens Systems (C): The lens system is responsible for collecting and focusing the incoming radiation onto the focal plane. It acts like a camera lens, creating a sharp image of the scene. Ground Resolution Cell (D): As previously defined, this is the smallest area on the ground that can be resolved by a remote sensing sensor. In the case of linear array scanne...

Discrete Detectors and Scanning mirrors Across the track scanner Whisk broom scanner.

Multispectral Imaging Using Discrete Detectors and Scanning Mirrors (Across-Track Scanner or Whisk Broom Scanner) Multispectral Imaging: This technique involves capturing images of the Earth's surface using multiple sensors that are sensitive to different wavelengths of electromagnetic radiation. This allows for the identification of various features and materials based on their spectral signatures. Discrete Detectors: These are individual sensors that are arranged in a linear or array configuration. Each detector is responsible for measuring the radiation within a specific wavelength band. Scanning Mirrors: These are optical components that are used to deflect the incoming radiation onto the discrete detectors. By moving the mirrors, the sensor can scan across the scene, capturing data from different points. Across-Track Scanner or Whisk Broom Scanner: This refers to the scanning mechanism where the mirror moves perpendicular to the direction of flight. This allows for t...

Vineesh V, Geography

Search This Blog