**2. Radar altimetry technology and principles**

This section gives the theoretical background on the altimeter principles and concepts, the development of the technology and the satellite missions, and current advances on altimeter data processing and product deriving.

#### **2.1 Concepts of satellite altimetry**

Conceptually, satellite altimeters measure the distance from the satellite to the sea-level surface, i.e., the range *R*, thus enabling deriving of the sea level surface referred to any desired geodetic reference frame such as the ellipsoid or the geoid. The altimeter transmits a short pulse of microwave radiation with known power towards the sea surface, where it interacts with the sea surface. The range is measured from a time taken for incident radiation of a signal to reflect back to the altimeter, which enables determining of the sea surface height. Eq. (1) presents the basic principle of satellite altimetry, i.e., the measuring of the range *R* from the round-trip travel time, without refraction accounted for, based on the speed of light in vacuum *c* :

$$
\hat{R} = \frac{ct}{2}.\tag{1}
$$

**79**

**Figure 1.**

*Radar Satellite Altimetry in Geodesy - Theory, Applications and Recent Developments*

combination with satellite and ground-based tracking systems. Satellite altimeters are usually equipped with GNSS and DORIS receivers to ensure onboard satellite tracking. Some of the altimeters are additionally equipped with star trackers, which give altitude and position information when GNSS is not available [11]. The ground tracking system is most often based on satellite laser ranging (SLR) tracking methods that provide satellite position from a global network of observation stations. Besides the on-board navigation devices and retroreflectors for laser tracking, satellites carry microwave radiometers, which usually operate on two or more frequencies. A radiometer is an instrument that measures radiant energy reflected from the oceans and serves to estimate the surface water vapor (see e.g., [12]). The measurements depend on surface winds, ocean and near-ocean air temperature,

*Satellite altimetry and related observation systems (tide gauge sea level measurements, interferometric synthetic aperture radar (InSAR), GNSS (global navigation satellite system), Doppler Orbitography and Radiopositioning integrated by satellite (DORIS) and satellite laser ranging (SLR)) shown in integrated* 

As shown in **Figure 1**, satellite altimeters are measuring ranges relative to the center of the Earth, i.e., to the reference ellipsoid. Satellites are flying in known pre-defined orbits *hOR* that are computed with respect to the fixed coordinate system hence enabling straightforward deriving of the Sea Surface Height (SSH),

> = − = −+ ∆ ∑ . *OR OR j*

The analyses of the shapes of signals returned from the sea surface are used for derivation of the Significant Wave Height (SWH) information. SWH is defined as four times the standard deviation of sea surface elevation and it corresponds to the average crest-to-trough height of 1/3 of the highest waves [6]. Therefore, it is often denoted as 1/3 *h* . Also, the sea roughness, which is correlated with surface wind

*j SSH h R h R R* (3)

salinity, foam, and the absorption by water vapor and clouds [7].

speed can be estimated from the power of the returned signal.

For more details, please see [6, 7].

which is related to a reference ellipsoid, from a measured range (Eq. (3)).

*DOI: http://dx.doi.org/10.5772/intechopen.97349*

*observation systems of the earth (adapted from [10]).*

After applying the corrections to the measurements, the basic equation can be modified to present corrected range *R* as [6, 9]:

$$R = \hat{R} - \sum\_{j} \Delta R\_{j} = \hat{R} - \left(\Delta R\_{\text{tropo}D} + \Delta R\_{\text{tropo}W} + \Delta R\_{\text{iono}} + \Delta R\_{\text{ad}} + \cdots\right) \tag{2}$$

where ∆ =… , 1, *R j <sup>j</sup>* is the sum of the atmospheric and technology corrections applied to the signal pulse, which encompasses dry and wet component of the tropospheric correction, *RtropoD* and *RtropoW* , ionospheric correction *Riono* , the influences of the ocean dynamics *Rod* , and the other corrections [6]. Due to such influences, the propagation of the signal through the atmosphere is slowed down, meaning that the corrections of the *R* are positive values. The accuracy of the range is, naturally, directly correlated to the accuracy of the corrections applied to derive the sea surface height.

The basic principles of the technology integrated with the other related remote sensing systems are shown in **Figure 1**. The accuracy of determining the satellite altimeter position is critical for the measurements of the range. The accurate position of the satellite is ensured through the precise orbit computations in

*Radar Satellite Altimetry in Geodesy - Theory, Applications and Recent Developments DOI: http://dx.doi.org/10.5772/intechopen.97349*

#### **Figure 1.**

*Geodetic Sciences - Theory, Applications and Recent Developments*

literature and points towards more specific studies.

**2. Radar altimetry technology and principles**

modified to present corrected range *R* as [6, 9]:

*j*

advances on altimeter data processing and product deriving.

than 3 hours after the acquisition).

**2.1 Concepts of satellite altimetry**

in vacuum *c* :

corrected using various atmospheric and geophysical models and corrections, up to complete products ready to use in different applications. The measurements are distributed with different timeliness, most often in near real-time (e.g., in less

This book chapter presents the theoretical background of the technology, basic principles and data processing procedures, current trends in technology, and different applications of the technology. The chapter gives an overview of the relevant

This section gives the theoretical background on the altimeter principles and concepts, the development of the technology and the satellite missions, and current

Conceptually, satellite altimeters measure the distance from the satellite to the sea-level surface, i.e., the range *R*, thus enabling deriving of the sea level surface referred to any desired geodetic reference frame such as the ellipsoid or the geoid. The altimeter transmits a short pulse of microwave radiation with known power towards the sea surface, where it interacts with the sea surface. The range is measured from a time taken for incident radiation of a signal to reflect back to the altimeter, which enables determining of the sea surface height. Eq. (1) presents the basic principle of satellite altimetry, i.e., the measuring of the range

round-trip travel time, without refraction accounted for, based on the speed of light

After applying the corrections to the measurements, the basic equation can be

= − ∆ = − ∆ +∆ +∆ +∆ + ∑ ( )

where ∆ =… , 1, *R j <sup>j</sup>* is the sum of the atmospheric and technology corrections

The basic principles of the technology integrated with the other related remote

sensing systems are shown in **Figure 1**. The accuracy of determining the satellite altimeter position is critical for the measurements of the range. The accurate position of the satellite is ensured through the precise orbit computations in

applied to the signal pulse, which encompasses dry and wet component of the tropospheric correction, *RtropoD* and *RtropoW* , ionospheric correction *Riono* , the influences of the ocean dynamics *Rod* , and the other corrections [6]. Due to such influences, the propagation of the signal through the atmosphere is slowed down, meaning that the corrections of the *R* are positive values. The accuracy of the range is, naturally, directly correlated to the accuracy of the corrections applied to derive

*<sup>j</sup> tropoD tropoW iono od*

*RR R R R R R R* (2)

. 2 =

*ct <sup>R</sup>* (1)

*R* from the

**78**

the sea surface height.

*Satellite altimetry and related observation systems (tide gauge sea level measurements, interferometric synthetic aperture radar (InSAR), GNSS (global navigation satellite system), Doppler Orbitography and Radiopositioning integrated by satellite (DORIS) and satellite laser ranging (SLR)) shown in integrated observation systems of the earth (adapted from [10]).*

combination with satellite and ground-based tracking systems. Satellite altimeters are usually equipped with GNSS and DORIS receivers to ensure onboard satellite tracking. Some of the altimeters are additionally equipped with star trackers, which give altitude and position information when GNSS is not available [11]. The ground tracking system is most often based on satellite laser ranging (SLR) tracking methods that provide satellite position from a global network of observation stations.

Besides the on-board navigation devices and retroreflectors for laser tracking, satellites carry microwave radiometers, which usually operate on two or more frequencies. A radiometer is an instrument that measures radiant energy reflected from the oceans and serves to estimate the surface water vapor (see e.g., [12]). The measurements depend on surface winds, ocean and near-ocean air temperature, salinity, foam, and the absorption by water vapor and clouds [7].

As shown in **Figure 1**, satellite altimeters are measuring ranges relative to the center of the Earth, i.e., to the reference ellipsoid. Satellites are flying in known pre-defined orbits *hOR* that are computed with respect to the fixed coordinate

system hence enabling straightforward deriving of the Sea Surface Height (SSH), which is related to a reference ellipsoid, from a measured range (Eq. (3)).

$$\text{SSH} = h\_{\text{OR}} - R = h\_{\text{OR}} - \hat{R} + \sum\_{j} \Delta R\_j. \tag{3}$$

The analyses of the shapes of signals returned from the sea surface are used for derivation of the Significant Wave Height (SWH) information. SWH is defined as four times the standard deviation of sea surface elevation and it corresponds to the average crest-to-trough height of 1/3 of the highest waves [6]. Therefore, it is often denoted as 1/3 *h* . Also, the sea roughness, which is correlated with surface wind speed can be estimated from the power of the returned signal.

For more details, please see [6, 7].
