Environmental Geodesy

Environmental GeodesyEnvironmental Geodesy

Lecture 3 (February 1, 2011): Earth's Shape- Earth's mean shape- Endogenic processes and Earth's shape- Exogenic processes and Earth's shape- Oceans, hydrosphere and cryosphere and Earth's shape

Lecture 3 (February 1, 2011): Earth's Shape- Earth's mean shape- Endogenic processes and Earth's shape- Exogenic processes and Earth's shape- Oceans, hydrosphere and cryosphere and Earth's shape

Earth's Mean ShapeEarth's Mean Shape

The meaning of the terms "figure of the Earth" and "shape of the Earth" depends on context, e.g. (1) topography of the solid Earth; (2) surface of solid Earth including oceans, terrestrial hydrosphere and cryosphere.


ETOPO1 includes ocean bottom topography and ice mass surfaces, i.e., it is in between (1) and (2).

ETOPO1 includes ocean bottom topography and ice mass surfaces, i.e., it is in between (1) and (2).

ETOPO1 Global Relief Model

ETOPO1 Global Relief Model




(2) is the surface on which most geodetic in situ measurements are carried out

(2) is the surface on which most geodetic in situ measurements are carried out

(2) is too complex for mathematical descriptions of characteristics of the solid Earth or the Earth system

(2) is too complex for mathematical descriptions of characteristics of the solid Earth or the Earth system

Soffel (1989) describes four different phases related to the view of the Earth's shape and dynamics and the main target of research (see Lecture 1).

Soffel (1989) describes four different phases related to the view of the Earth's shape and dynamics and the main target of research (see Lecture 1).


Four different phases of geodesy related to the view of the Earth's shape and dynamics and the main targets of research.

Four different phases of geodesy related to the view of the Earth's shape and dynamics and the main targets of research.

A: From 200 BC up to the middle of the 17th century: the radius of a spherical Earth; simple geometrical form.

A: From 200 BC up to the middle of the 17th century: the radius of a spherical Earth; simple geometrical form.

B: From the middle of the 17th century to the middle of the 19th century: the oblateness of a rotational ellipsoid; geometrical form resulting from rotational dynamics.


C: From the middle of the 19th century to the middle of the 20th century: the geoid; gravitational field in addition to a purely geometrical form.

C: From the middle of the 19th century to the middle of the 20th century: the geoid; gravitational field in addition to a purely geometrical form.

D: Since the middle of the 20th century: dynamics of the Earth's surface and relativistic models of the Earth system; changes in the shape instead of mean shape; dynamical instead of static view.

D: Since the middle of the 20th century: dynamics of the Earth's surface and relativistic models of the Earth system; changes in the shape instead of mean shape; dynamical instead of static view.




Rotational ellipsoid is uniquely defined by two numbers:- two dimensions (i.e., two axes), - one dimension (axis0 and a number representing the difference between the two dimensions.







Geodesists, by convention, use the semimajor axis and flattening: - Size of ellipsoid: radius a at the equator; i.e. semimajor axis of the cross-sectional ellipse- Shape of the ellipsoid: flattening f, which indicates how much the ellipsoid departs from spherical.

Geodesists, by convention, use the semimajor axis and flattening: - Size of ellipsoid: radius a at the equator; i.e. semimajor axis of the cross-sectional ellipse- Shape of the ellipsoid: flattening f, which indicates how much the ellipsoid departs from spherical.

Long sequence of attempts to determine accurate values for a and f.Long sequence of attempts to determine accurate values for a and f.


A key open question relates to rotational ellipsoid: - Is the rotational figure of the Earth in hydrostatic equilibrium?

A key open question relates to rotational ellipsoid: - Is the rotational figure of the Earth in hydrostatic equilibrium?

Rotation of the Earth is decreasing (LOD increasing) over time (due to tidal friction):LLR: +2.3 ms/cy (cy=century)Historical record of eclipses: +1.70 ± 0.05 ms/cyThis indicates a quadratic term: +31 s/cy²

Rotation of the Earth is decreasing (LOD increasing) over time (due to tidal friction):LLR: +2.3 ms/cy (cy=century)Historical record of eclipses: +1.70 ± 0.05 ms/cyThis indicates a quadratic term: +31 s/cy²

Question relates to the "Love Number" k2 (will be explained later), which is

relevant for many secular geodynamic problems

Question relates to the "Love Number" k2 (will be explained later), which is

relevant for many secular geodynamic problems

As a result, oblateness should be decreasing, depending on the viscoelastic response of the Earth to the changing gravitational potential .SLR:

As a result, oblateness should be decreasing, depending on the viscoelastic response of the Earth to the changing gravitational potential .SLR:


Topography deviates from reference ellipsoid by +8848 m and -10,911 m - deviations are small (only 0.17% of the radius)- deviations are relevant for many practical applications

Topography deviates from reference ellipsoid by +8848 m and -10,911 m - deviations are small (only 0.17% of the radius)- deviations are relevant for many practical applications

Geoid deviates from reference ellipsoid by about -110 m and +85 m. Geoid deviates from reference ellipsoid by about -110 m and +85 m.

Geoid is a equipotential surface of Earth's gravitational potential (including both gravitational and centrifugal forces).

Geoid is a equipotential surface of Earth's gravitational potential (including both gravitational and centrifugal forces).

Sea level - adjusts to gravitation field, not geometry;- it follows a equipotential surface of the gravitational potential, if undisturbed by tides, winds, currents, ...

Sea level - adjusts to gravitation field, not geometry;- it follows a equipotential surface of the gravitational potential, if undisturbed by tides, winds, currents, ...


Geoid deviates from reference ellipsoid by about -110 m and +85 m. Geoid deviates from reference ellipsoid by about -110 m and +85 m.


Improvement of the Earth’s gravity field models. From top left to bottom right:

GRIM-5S1: SLR data only (best gravity field model before CHAMP and GRACE);

EIGEN-CHAMP03S: Gravity field from CHAMP;

EIGEN-GRACE03S: Gravity field from GRACE;

EIGEN-CG03C: Gravity field from GRACE combined with terrestrial data.

Improvement of the Earth’s gravity field models. From top left to bottom right:

GRIM-5S1: SLR data only (best gravity field model before CHAMP and GRACE);

EIGEN-CHAMP03S: Gravity field from CHAMP;

EIGEN-GRACE03S: Gravity field from GRACE;

EIGEN-CG03C: Gravity field from GRACE combined with terrestrial data.

Reigber et al. (2005).Reigber et al. (2005).


"Mean" dynamic sea surface topography due to influences of ocean circulation, ocean temperature, salinity.

"Mean" dynamic sea surface topography due to influences of ocean circulation, ocean temperature, salinity.

After removing tides, waves, atmospheric forcing (including surges), sea level can deviate up to 2 m from the geoid.

After removing tides, waves, atmospheric forcing (including surges), sea level can deviate up to 2 m from the geoid.

Accurate "static' geoid required for determination of mean dynamic sea surface topography, which is required for ocean circulation and climate models.

Accurate "static' geoid required for determination of mean dynamic sea surface topography, which is required for ocean circulation and climate models.

Currently, most accurate static geoid from the Gravity Recovery and Climate Experiment (GRACE).

Currently, most accurate static geoid from the Gravity Recovery and Climate Experiment (GRACE).

Significant improvements of static geoid expected from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) .

Significant improvements of static geoid expected from the Gravity field and steady-state Ocean Circulation Explorer (GOCE) .

GRACE is particularly strong in measuring geoid variations at sub-monthly time scales and down to 300 km spatial scales (see Lecture 4).

GRACE is particularly strong in measuring geoid variations at sub-monthly time scales and down to 300 km spatial scales (see Lecture 4).


Significant improvements expected from the Gravity field and steady-state Ocean Circulation Explorer (GOCE).

Significant improvements expected from the Gravity field and steady-state Ocean Circulation Explorer (GOCE).

Launched on 17 March 2009. Launched on 17 March 2009.


Relation of the various surfaces used in geodesy Relation of the various surfaces used in geodesy 1. Ocean

2. Ellipsoid

3. Local plumb

4. Continent

5. Geoid

1. Ocean

2. Ellipsoid

3. Local plumb

4. Continent

5. Geoid

Endogenic ProcessesEndogenic Processes

Endogenic processes change the Earth shape on time scales from seconds to million of years

Endogenic processes change the Earth shape on time scales from seconds to million of years


Earthquakes cause significant 3-d deformations within seconds to minutesEarthquakes cause significant 3-d deformations within seconds to minutes


A 2.3 m coseismic displacement has distorted the railroad track near the railway station Tepetarla in the region between Sapanca Lake and Izmir Gulf, Turkey (www.geopages.co.uk/news/rev002.html).

A 2.3 m coseismic displacement has distorted the railroad track near the railway station Tepetarla in the region between Sapanca Lake and Izmir Gulf, Turkey (www.geopages.co.uk/news/rev002.html).


Earthquakes cause significant "static"/permanent 3-d deformations within seconds to minutes.

Earthquakes cause significant "static"/permanent 3-d deformations within seconds to minutes.

Predicted coseismic displacement field of the Sumatra-Andaman 2004 earthquake.Predicted coseismic displacement field of the Sumatra-Andaman 2004 earthquake.


GPS observes the static, co-seismic offset

GPS observes the static, co-seismic offset

Observed coseismic displacement field of the Sumatra-Andaman 2004 earthquake.Observed coseismic displacement field of the Sumatra-Andaman 2004 earthquake.

Large tsunamis are associated with loading signals on the order of 10 mm

Large tsunamis are associated with loading signals on the order of 10 mm


April 4, 2010 Mayor-Cucapah M 7.2 earthquake

April 4, 2010 Mayor-Cucapah M 7.2 earthquake

Seismic waves have amplitudes of several > 100 mm in large distances from the epicenter

Seismic waves have amplitudes of several > 100 mm in large distances from the epicenter


Displacement field of Hector Mine earthquake observed with InSAR

Displacement field of Hector Mine earthquake observed with InSAR

G. Peltzer, UCLAG. Peltzer, UCLA


More on earthquakes; goal to give an impression of the changes in earth shape ...

More on earthquakes; goal to give an impression of the changes in earth shape ...


Seismic Free Oscillations of the Earth deform the earth with periods from 53 minutes down to seconds and can last for several days.

Seismic Free Oscillations of the Earth deform the earth with periods from 53 minutes down to seconds and can last for several days.

http://icb.u-bourgogne.fr/Nano/MANAPI/saviot/terre/index.en.htmlhttp://icb.u-bourgogne.fr/Nano/MANAPI/saviot/terre/index.en.html

Theoretical representation through spherical harmonics.Theoretical representation through spherical harmonics.


Seismic Free Oscillations of the Earth deform the earth with periods from 53 minutes down to seconds

Seismic Free Oscillations of the Earth deform the earth with periods from 53 minutes down to seconds

http://icb.u-bourgogne.fr/Nano/MANAPI/saviot/terre/index.en.htmlhttp://icb.u-bourgogne.fr/Nano/MANAPI/saviot/terre/index.en.html

Theoretical representation through spherical harmonics.Theoretical representation through spherical harmonics.


More on post-seismic deformationsMore on post-seismic deformations


InSAR (ERS) has revealed that four Andean volcanoes thought to be inactive, are now known to be rapidly deforming. Each color cycle corresponds to 5 cm of deformation.

The top three volcanoes are inflating and Robledo is deflating

(Pritchard & Simons, 2002).

InSAR (ERS) has revealed that four Andean volcanoes thought to be inactive, are now known to be rapidly deforming. Each color cycle corresponds to 5 cm of deformation.

The top three volcanoes are inflating and Robledo is deflating

(Pritchard & Simons, 2002).

Subsurface processes associated with volcanoes and magma transport induce local to regional changes in shape.

Subsurface processes associated with volcanoes and magma transport induce local to regional changes in shape.


Plate tectonics induce secular changes in shape on the order of 10 cm/yr horizontally

Plate tectonics induce secular changes in shape on the order of 10 cm/yr horizontally


Secular changesSecular changes


Secular strain rates caused by plate tectonics and plate boundary processes

Secular strain rates caused by plate tectonics and plate boundary processes

Kreemer et al. (2003)Kreemer et al. (2003)

Exogenic ProcessesExogenic Processes

Exogenic variations in Earth's shape include:- Tides of the solid Earth caused by the tidal potential of moon, sun, and planets (see Lecture 4); - Rotational perturbations caused by exchange of momentum between core and mantle, angular momentum exchange with atmosphere and ocean, external torque caused by tidal forces, ... (see Lecture 5);- surface loading due to mass relocation on the Earth's surface.

Exogenic variations in Earth's shape include:- Tides of the solid Earth caused by the tidal potential of moon, sun, and planets (see Lecture 4); - Rotational perturbations caused by exchange of momentum between core and mantle, angular momentum exchange with atmosphere and ocean, external torque caused by tidal forces, ... (see Lecture 5);- surface loading due to mass relocation on the Earth's surface.


Surface loading due to mass relocation on the Earth's surface include:- mass redistribution in atmosphere: low/high pressure areas;- mass relocation in the ocean: tsunamis, tides, storm surges, wind-driven circulation, other circulation;- redistribution of water stored on land;- mass changes in land-based glaciers, ice caps and ice sheets;- mass exchange between any of these reservoirs in the global water cycle;- sediment transport and deposition;- anthropogenic mass relocation (coal mining, oil mining, groundwater mining, ...)

Surface loading due to mass relocation on the Earth's surface include:- mass redistribution in atmosphere: low/high pressure areas;- mass relocation in the ocean: tsunamis, tides, storm surges, wind-driven circulation, other circulation;- redistribution of water stored on land;- mass changes in land-based glaciers, ice caps and ice sheets;- mass exchange between any of these reservoirs in the global water cycle;- sediment transport and deposition;- anthropogenic mass relocation (coal mining, oil mining, groundwater mining, ...)

Loading - deforms the solid Earth, - changes the gravity field (both due to the surface mass relocation and the deformation of the solid Earth) and - impacts Earth rotation.

Loading - deforms the solid Earth, - changes the gravity field (both due to the surface mass relocation and the deformation of the solid Earth) and - impacts Earth rotation.


Response of solid Earth has an elastic (instantaneous) and viscous (delayed) contribution.

Response of solid Earth has an elastic (instantaneous) and viscous (delayed) contribution.

Elastic response dominate for loading at sub-seasonal to interannual time scales (e.g., tides, seasonal cycle);Viscous contribution important for interannual to secular time scales (e.g. coal mining, postglacial rebound).

Elastic response dominate for loading at sub-seasonal to interannual time scales (e.g., tides, seasonal cycle);Viscous contribution important for interannual to secular time scales (e.g. coal mining, postglacial rebound).

Elastic deformations range from up to 20 mm for atmospheric loading, 50 mm associated with ocean loading (tides and surges); Visco-elastic deformations range from sub-mm/yr for hydrologic changes (droughts), 1 mm/yr in coal mining areas, several mm/yr for recent ice load changes, more than 50 mm/yr during major deglaciation periods.

Elastic deformations range from up to 20 mm for atmospheric loading, 50 mm associated with ocean loading (tides and surges); Visco-elastic deformations range from sub-mm/yr for hydrologic changes (droughts), 1 mm/yr in coal mining areas, several mm/yr for recent ice load changes, more than 50 mm/yr during major deglaciation periods.

Post-mass relocation deformations are triggered by surface loads but then dominated by endogenic processes.

Post-mass relocation deformations are triggered by surface loads but then dominated by endogenic processes.

More details on this during subsequent lectures.More details on this during subsequent lectures.

Oceans, Cryosphere, and Terrestrial Hydrosphere Oceans, Cryosphere, and Terrestrial Hydrosphere

Oceans: - Time-variable surface, both as spatial average and locally- global sea level variations caused by mass exchange with other reservoirs and changes in heat contents, - variability on a wide range of spatial and temporal scales

Oceans: - Time-variable surface, both as spatial average and locally- global sea level variations caused by mass exchange with other reservoirs and changes in heat contents, - variability on a wide range of spatial and temporal scales

Ice surfaces:- Time-variable surface height and extent;- large variations in mass balance;- seasonal, interannual, decadal time scales;- ice ages on time scales of 100 kyrs.

Ice surfaces:- Time-variable surface height and extent;- large variations in mass balance;- seasonal, interannual, decadal time scales;- ice ages on time scales of 100 kyrs.

Land water storage:- Time-variable surface water storage (e.g., floods, droughts), also including significant anthropogenic changes; - Time-variable subsurface water storage (includes also significant anthropogenic changes)

Land water storage:- Time-variable surface water storage (e.g., floods, droughts), also including significant anthropogenic changes; - Time-variable subsurface water storage (includes also significant anthropogenic changes)

Oceans, Cryosphere, and Terrestrial Hydrosphere Oceans, Cryosphere, and Terrestrial Hydrosphere

More details in subsequent lectures.More details in subsequent lectures.

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