**1. Introduction**

Water that is present in different forms in the Earth's system ensures the global transport of the solar heat in the oceans and atmosphere, and thus maintains life development. As it represents a precious resource, in particular for human activities, monitoring the water cycle from space remains important for its management and understanding climate change. Observation of the Earth from space, and the determination of its gravity fields in particular, provide precious information on the mass transfers in any part of the globe.

Global gravity field models are based on the theoretical expression of the variations of the geopotential V:

*Geodetic Sciences - Theory, Applications and Recent Developments*

$$V(\boldsymbol{\lambda}, \boldsymbol{\theta}, r) = \frac{GM}{a\_{\boldsymbol{\epsilon}}} \sum\_{n=0}^{n} \left(\frac{a\_{\boldsymbol{\epsilon}}}{r}\right)^{n+1} \sum\_{m=0}^{n} P\_{nm}(\sin \theta) \left(\mathbb{C}\_{nm} \cos m\boldsymbol{\lambda} + \mathbb{S}\_{nm} \sin m\boldsymbol{\lambda}\right) \tag{1}$$

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 ∙105 m3 /s2 , 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 -, and/or satellite velocities [1].

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.

#### **Figure 1.**

*Time variations of the C20 coefficient (representing Earth's flatness) determined by analysis of the LAGEOS 1 & 2 satellite telemetry (source: GRGS, Toulouse).*

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**Figure 2.**

*Continental Water Storage Changes Sensed by GRACE Satellite Gravimetry*

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

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,

The GRACE mission consists of two 0.5 ton satellites that followed each other at a distance of ~220 km, which were placed at a relatively low average altitude of around 450 km with a quasi-polar orbit inclination of 89.5 degrees to ensure a quasi-global coverage (**Figure 2**). The relative distance between the two satellites was measured with a accuracy of 1 μm.s−1 by a radar telemeter operating at K-Band microwave Ranging (KBR) [4]. The inter-satellite distance depends of the gravitational acceleration changes that affect each GRACE satellite [6]. The A three-axis accelerometer that senses the dynamical effects as non-dissipative forces (the mean solar and Earth's radiation pressure, the atmospheric drag) is also placed on-board. Afterwards the non-gravitational effects are removed from the raw accelerations, the geopotential change along the track of the GRACE satellites is estimated from the residual perturbations in distance and inter-satellite distance changing rate. Changes of the observed inter-satellite distances reflect the variations of the Earth's

ice mass lost in Polar regions as a consequence of global warming [5].

**2. GRACE mission orbit and its on-board instruments**

gravity field related to topography and density heterogeneities.

*Artistic view of the twin GRACE vehicles orbiting around the earth (source: NASA [7]).*

*DOI: http://dx.doi.org/10.5772/intechopen.96109*

of the world.
