*Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry DOI: http://dx.doi.org/10.5772/intechopen.96109*

*Geodetic Sciences - Theory, Applications and Recent Developments*

*a r*

∑ ∑

λ θ

and/or satellite velocities [1].

∙105 m3 /s2 ( ) ( )( )

where *λ* and *θ* are the longitude and the latitude of the observation point respectively, *r* is the radial distance from the Earth's center to the point of observation, *P*nm is the associate Legendre function of degree n and order m, ae is the equatorial Earth's radius and the gravitational parameter is the product of the gravitational constant *G* with the total mass of the Earth M, so that *GM* = 3.986004410 ∙ 1014+/−8

, according to IERS Standard. Space geodesy consists of determining the dimensionless Stokes coefficients *C*nm and *S*nm of the gravity field model as precisely as possible using combined satellite data and terrestrial gravity measurements on lands. As the satellite motion depends mainly on the gravitational field according to the Newton's law of attraction (~99% of the sensed gravity signal is from the solid Earth part), the only remote sensing technique to measure variations of water mass quantity is based on inversion of very precise satellite positions - with an accuracy of at least a few cm for detecting long wavelengths of the continental hydrology -,

Historically, long wavelengths of the gravity field time variations were determined using very precise Satellite Laser Ranging (SLR) data of 5900-km altitude LAGEOS 1–2 trajectories that reveal the movements of the center of mass of the Earth (or "geocenter") representing a few thousands of mm, and Earth's flatness due to seasonal mass exchange between the two hemispheres and the regular decrease due to post-glacial rebound occurring since 20 000 years [2] (**Figure 1**). Since the beginning of the 21st century, a new generation of passive and quasipolar Low-Earth-Orbit (LEO) satellites has been launched to improve the spatial resolution of global gravity field models: the CHAllenging Mini-satellite Payload (CHAMP, 2000–2010) mission operated by the DLR in Germany, and the Gravity field and steady-state Ocean Circulation Explorer (GOCE, 2009–2013) of ESA.

*Time variations of the C20 coefficient (representing Earth's flatness) determined by analysis of the LAGEOS 1* 

θ

*nm nm nm*

λλ

(1)

, , sin cos sin

*GM <sup>a</sup> V r P C mS m*

<sup>=</sup> <sup>+</sup>

1

*n n e*

0 0

= =

*e n m*

+ ∞

**60**

**Figure 1.**

*& 2 satellite telemetry (source: GRGS, Toulouse).*

As the CHAMP mission represents its precursor, the main scientific objective of the Gravity Recovery And Climate Experiment (GRACE, 2002–2017) mission proposed by the American National Aeronautics and Space Administration (NASA) and the German Aerospace Center Deutsches Zentrum für Luft- und Raumfahrt (DLR), was to measure both static and time-varying gravity field acting in different regions of the world.

GRACE was the first mission to use the principle of two co-orbital identical satellites in pursuit, as initially proposed by [3] for estimating the spatial and temporal variations of the gravitational field which reflect mass changes in the Earth system over time scales ranging from months to a ten of years [4], so that GRACE observation represents the sum of the effects of all changes in mass which are radially integrated. In fact, GRACE observations are used to successfully survey the continental hydrology at different time scales (decanal, seasonal, rapid events) allowing to measure the climate change impacts in the Earth system, as for example, ice mass lost in Polar regions as a consequence of global warming [5].
