**2. Integrated precipitable water vapour**

Water vapour is one of the main constituents of the atmosphere and its accurate and frequent sampling is obviously of great use for climatological research as well as operational weather forecasting. Moreover, water vapour is one of the most variable atmospheric constituents, fundamental in the transfer of energy in atmosphere: improving knowledge of its distribution is fundamental to set good initial conditions in numerical weather forecast. In addition, water vapor fluctuations are a major error source in ranging measurements through the Earth's atmosphere, and therefore the principal limiting factor in space geodesy applications such as GNSS, very long baseline interferometry, satellite altimetry, and

obtainable can be found in Anthes et al. (2008) and Luntama et al. (2008)) a mention is due. When signals cross in this way the atmosphere, they are delayed and their path is bent: therefore, the signal can be received also below the terrestrial limb, when the satellites are not yet in view. GNSS Radio Occultation is based on the inversion of the excess-phase (carrier phase in excess with respect the one experienced considering vacuum propagation) and amplitude evolution measured on the received signal when it is "occulted" with respect to the transmitter. Applying Geometric Optics algorithms or Wave Optics algorithm and Fourier operators to such observables, time evolutions of two important parameters identifying each trajectory followed by the signal can be derived: its total bending and its impact parameter, which is the distance of the trajectory asymptotes from the Earth's mass centre. Such quantities are in turn related to the integral of the atmospheric refraction index vertical profile, in a mathematical formulation that is invertible in a closed form. Result of the inversion is a veryaccurate and high-resolved (up to about 100 m) atmospheric refractivity vertical profile, from

The second technique described in this chapter adds a further spatial variability characterization possibility with respect to that given by IPWV and Radio Occultation. It deals with the three-dimensional reconstruction of atmospheric refractivity and, thus, water vapour density, applying tomographic techniques to phase delays measurements collected by small (but dense) networks of GPS receivers. Because of volume dimensions, inhomogeneity spatial distribution and geometric constraints, all the weak points of tomography emerge in characterizing neutral atmospheric parameter distributions using

The last application we will describe (section 4) is the most recent and maybe the most challenging one. It foresees the use of GNSS signals reflected off from lands and oceans for characterizing the Earth's surface at L-band frequencies. The signal is received under bistatic geometry since the received signal power is that which is forward scattered from the Earth's surface towards the GNSS-R (GNSS-Reflectometry) receiver. The reflected signal contains many differences with respect to the direct one, in terms of delay, Doppler shift, power strength and polarization. Once the reflected signal is received, it is processed using hardware or software correlators. The reflecting surface features are dipped inside the shape, the magnitude and the maxima location (which is related to the propagation delay) of the obtained correlation function. Among the possible remote sensing applications we list: ocean altimetry (from delay); wind speed and ocean scatterometry (from shape and spreading), ice topography and monitoring (from delay and magnitude); soil moisture (from magnitude).

Water vapour is one of the main constituents of the atmosphere and its accurate and frequent sampling is obviously of great use for climatological research as well as operational weather forecasting. Moreover, water vapour is one of the most variable atmospheric constituents, fundamental in the transfer of energy in atmosphere: improving knowledge of its distribution is fundamental to set good initial conditions in numerical weather forecast. In addition, water vapor fluctuations are a major error source in ranging measurements through the Earth's atmosphere, and therefore the principal limiting factor in space geodesy applications such as GNSS, very long baseline interferometry, satellite altimetry, and

which the corresponding temperature and humidity profiles can be inferred.

GNSS signals. Results and comments are given in section 3.

**2. Integrated precipitable water vapour** 

Interferometric Synthetic Aperture Radar (InSAR). Several techniques are well established to derive the vertically Integrated Precipitable Water Vapor (IPWV)1, in particular using ground-based and spaced-based radiometers, radiosonde observations and GNSS receivers.

Radiosonde observations produce an accurate measurement of the water vapour profile, but the temporal and spatial resolution is rather poor. Radiosondes are typically launched every 6 to 12 hours, which may cause significant variations in water vapour to go undetected.

Ground-based microwave radiometers show problems during periods of rain fall and spacebased radiometer observations can be degraded in the presence of clouds. This prevents reliable measurements during periods where changes in water vapour could be quite great. Besides these limitations, all systems involve considerable costs.

The technique to estimate IPWV by means of GNSS receivers is based on measurements of the tropospheric delay time of navigation signals. Therefore the delay, regarded as a nuisance parameter by geodesists, can be directly related to the amount of water vapour in the atmosphere, and hence is a product of considerable value for meteorologists. Furthermore, water vapour estimation with ground-based GNSS receivers is not affected by rain fall and clouds, and can therefore be considered an all-weather system.

So, GNSS is a valuable complement to radiosondes and radiometers, taking into account that GNSS IPWV estimates come from an existing GNSS infrastructure and frequently from quite dense receiver networks.

### **2.1 Description of observables, theoretical basis and retrieval technique**

The use of GNSS receivers to estimate IPWV is based on measurements of the delay affecting the navigation signals during their propagation in troposphere (neutral atmosphere) from the GNSS satellites to the receivers on ground. The dispersive ionospheric effect can be removed with a good level of accuracy by a linear combination of dual frequency data.

Such a technique is founded on the non-dispersive refractive characteristics of the neutral atmosphere, governed by its composition. The water vapour molecules in atmosphere are polar in nature possessing a permanent dipole moment. All the other gases are non-polar molecules and a dipole moment is induced among these gases when microwave propagates through atmosphere. These molecules reorient themselves according to the polarity of propagating wave. In the retrieval technique to be described the atmosphere is considered as the sum of a dry component (mainly due to O2) and a wet component.

Consequently, the neutral delay due to the troposphere can be decomposed into the hydrostatic delay associated with the induced dipole moment of the atmosphere constituents and the wet delay associated with the permanent dipole moment of water vapour (Askne & Nordius, 1987; Brunner & Welsch, 1993; Treuhaft & Lanyi, 1987). The zenith hydrostatic delay (ZHD) has a typical magnitude of about 2.4 m at sea level, and it grows with increasing zenith angle reaching about 9.3 m for elevation angle of 15°. With

<sup>1</sup> Consider the total amount of atmospheric water vapour contained in a vertical column of unit cross section: if this water vapour were to condensate and precipitate, the equivalent height of the liquid water within the column is the Integrated Precipitable Water Vapour, usually measured in cm or in g/cm2

GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 175

*<sup>P</sup> ZHD k Z ds*

1. We start with the estimation of the neutral zenith path delay from GNSS observations (Bevis et al., 1992), which are elaborated using a specific GNSS software (e.g. Bernese GPS software or others). The neutral radio path delay has to be estimated using precise orbit ephemerides, choosing a proper cut-off angle (e.g. 15 degrees), resolution time (e.g. 30 minutes), and a suitable law as dry and wet mapping functions. Different kinds of mapping functions exist and they are different in number of meteorological

2. Computation of the ZHD component of the atmosphere, that is the greater component

If atmospheric profiles of temperature and dry pressure are available near the GPS station, the ZHD can be computed using eq. 4. Since such an availability is difficult in time and space, alternative and more simple procedures can be adopted for a reliable estimation of

If surface pressure is known with an accuracy of 0.3 hPa or better, *ZHD* can be estimated through simple models to better than 1 mm (Elgered et al., 1991), e.g. using the

0.22768 <sup>Z</sup> f , *HD Ps*

f( ) λ, 1 0.00266 cos 2 0.00028 *H H* =− ⋅ − ( ) ( )

where ZHD depends on actual surface pressure Ps (hPa), on latitude λ (rad) and on the surface height H (km). The error introduced by the assumption of hydrostatic equilibrium in the model formulation is typically of the order of 0.01%, corresponding to 0.2 mm in the

Typical values for the parameter П are approximately 0.16, so 6 mm of ZWD is equivalent to

The parameter П is a function of various physical constants and of the weighted mean

temperature Tm of the atmosphere (Askne & Nordius, 1987; Davis et al., 1985):

( )

*<sup>H</sup>* <sup>=</sup> (6)

*IPWV* = × *Π ZWD* (8)

(7)

λ

λ

In the estimation algorithm of IPWV we can identify four principal steps:

parameters involved (Herring, 1992; Ifadis, 1986; Niell, 1996).

in magnitude of ZTD but it is less variable with respect to ZWD.

and the wet part is:

the hydrostatic delay.

zenith delay.

about 1 mm of IPWV.

Saastamoinen model (Saastamoinen, 1972):

3. Then ZWD is computed by subtracting ZHD from ZTD. 4. Finally, it is possible to retrieve IPWV using the relationship:

6 1 <sup>1</sup> 10 *<sup>d</sup>*

*T*

6 16 1 2 3 <sup>2</sup> 10 10 *w w e e ZWD k Z ds k Z ds*

*T T*

*d*

− − = ⋅ (4)

− −− − =⋅ +⋅ (5)

simple models and accurate surface pressure measurements, it is usually possible to predict accurately the ZHD. The zenith wet delay (ZWD) can vary from a few millimeters in very arid condition to more than 350 mm in very humid condition, and it is not reliable to predict the wet delay with an useful degree of accuracy from surface measurements of pressure, temperature and humidity.

Therefore, from GNSS radio signals the total tropospheric delay is provided and, measuring the ZHD, it is possible to retrieve the remaining ZWD, incorporating mapping functions which describe the dependence on path orientation. The ZWD time series are then directly transformed into an estimate of IPWV: GNSS receivers can estimate IPWV with a temporal resolution of 30 min or better and with an accuracy better than 0.15 cm.

#### **2.1.1 Retrieval algorithm**

In this section the retrieval algorithm used for the estimation of IPWV from GNSS observations is presented.

Using GNSS methods of path delay correction, developed for geodetic applications, it is possible to estimate time-varying atmospheric zenith neutral delay ZTD (excess path length due to signal travel in the troposphere at zenith) defined as:

$$\text{ZTD} = \text{ZHD} + \text{ZVDD} = 10^{-6} \int\_{H}^{\text{ox}} N(\text{s})d\text{s} \tag{1}$$

where ds has units of length in the zenith, H is the surface height and N(s), usually expressed in parts per million (ppm), is the refractivity of air given by (Thayer, 1974):

$$N = k\_1(\frac{P\_d}{T})Z\_d^{-1} + k\_2(\frac{e}{T})Z\_w^{-1} + k\_3(\frac{e}{T^2})Z\_w^{-1} \tag{2}$$

where Pd is the dry air pressure (hPa), T is the air temperature (K), e is the partial pressure of water vapour (hPa), Zd and Zw are the dry air and water vapour compressibility factors, that consider the departure of air from an ideal gas. Values for inverse dry and wet compressibility factors differ from unity of about one part per thousand, and are given by:

$$\begin{aligned} Z\_d^{-1} &= 1 + P\_d \left[ 57.90 \cdot 10^{-8} \left( 1 + \frac{0.52}{T} \right) - 9.4611 \cdot 10^{-4} \frac{T\_c}{T^2} \right] \\ Z\_w^{-1} &= 1 + 1650 \cdot \left( \frac{e}{T^3} \right) \left( 1 - 0.01317 \cdot T\_c + 1.75 \cdot 10^{-4} \cdot T\_c^2 + 1.44 \cdot 10^{-6} \cdot T\_c^3 \right) \end{aligned} \tag{3}$$

where Tc is temperature in Celsius.

Several authors have given values for the empiric constants k1, k2 and k3 of eq. 2: a typical choice is k1=77.604 (K⋅ hPa-1), k2=64.79 (K⋅ hPa-1) and k3=3.776⋅105(K2⋅hPa-1) (Thayer, 1974).

In eq. 2, the first two terms of N are due to the induced dipole effect of the neutral atmospheric molecules (dry gases and water vapour), and the third term is caused by the permanent dipole moment of the water vapour molecule. Therefore, the hydrostatic part is described by:

$$ZHD = 10^{-6} \cdot k\_1 \int \frac{P\_d}{T} Z\_d^{-1} ds \tag{4}$$

and the wet part is:

174 Remote Sensing of Planet Earth

simple models and accurate surface pressure measurements, it is usually possible to predict accurately the ZHD. The zenith wet delay (ZWD) can vary from a few millimeters in very arid condition to more than 350 mm in very humid condition, and it is not reliable to predict the wet delay with an useful degree of accuracy from surface measurements of pressure,

Therefore, from GNSS radio signals the total tropospheric delay is provided and, measuring the ZHD, it is possible to retrieve the remaining ZWD, incorporating mapping functions which describe the dependence on path orientation. The ZWD time series are then directly transformed into an estimate of IPWV: GNSS receivers can estimate IPWV with a temporal

In this section the retrieval algorithm used for the estimation of IPWV from GNSS

Using GNSS methods of path delay correction, developed for geodetic applications, it is possible to estimate time-varying atmospheric zenith neutral delay ZTD (excess path length

*ZTD ZHD ZWD N s ds*

where ds has units of length in the zenith, H is the surface height and N(s), usually

1 23 <sup>2</sup> ( ) () ( ) *<sup>d</sup> dw w*

where Pd is the dry air pressure (hPa), T is the air temperature (K), e is the partial pressure of water vapour (hPa), Zd and Zw are the dry air and water vapour compressibility factors, that consider the departure of air from an ideal gas. Values for inverse dry and wet compressibility factors differ from unity of about one part per thousand, and are given by:

1 42 63

1 1650 1 0.01317 1.75 10 1.44 10

*<sup>e</sup> <sup>Z</sup> TT T*

− − −

*w cc c*

Several authors have given values for the empiric constants k1, k2 and k3 of eq. 2: a typical choice is k1=77.604 (K⋅ hPa-1), k2=64.79 (K⋅ hPa-1) and k3=3.776⋅105(K2⋅hPa-1) (Thayer, 1974). In eq. 2, the first two terms of N are due to the induced dipole effect of the neutral atmospheric molecules (dry gases and water vapour), and the third term is caused by the permanent dipole moment of the water vapour molecule. Therefore, the hydrostatic part is

=+ ⋅ − ⋅ + ⋅ ⋅ + ⋅ ⋅

*<sup>P</sup> e e Nk Z k Z k Z T T T*

expressed in parts per million (ppm), is the refractivity of air given by (Thayer, 1974):

18 4

*<sup>T</sup> Z P*

−− −

0.52 1 57.90 10 1 9.4611 10

*<sup>c</sup> d d*

=+ ⋅ + − ⋅

3

*T*

where Tc is temperature in Celsius.

described by:

<sup>6</sup> 10 ( ) *H*

( )

*T T*

11 1

<sup>−</sup> =+ = (1)

−− − = ++ (2)

2

(3)

∞

resolution of 30 min or better and with an accuracy better than 0.15 cm.

due to signal travel in the troposphere at zenith) defined as:

temperature and humidity.

**2.1.1 Retrieval algorithm** 

observations is presented.

$$Z\text{VMD} = 10^{-6} \cdot k\_2 \int \frac{\mathcal{e}}{T} Z\_w^{-1} ds + 10^{-6} \cdot k\_3 \int \frac{\mathcal{e}}{T^2} Z\_w^{-1} ds \tag{5}$$

In the estimation algorithm of IPWV we can identify four principal steps:


If atmospheric profiles of temperature and dry pressure are available near the GPS station, the ZHD can be computed using eq. 4. Since such an availability is difficult in time and space, alternative and more simple procedures can be adopted for a reliable estimation of the hydrostatic delay.

If surface pressure is known with an accuracy of 0.3 hPa or better, *ZHD* can be estimated through simple models to better than 1 mm (Elgered et al., 1991), e.g. using the Saastamoinen model (Saastamoinen, 1972):

$$\text{ZHD} = \stackrel{0.22768}{\text{}} \bigvee\_{\text{f}} \text{(\$\mathcal{X}\_{\text{'}}\$H\$)}\tag{6}$$

$$\mathbf{f}(\lambda, H) = \left(1 - 0.00266 \cdot \cos(2\lambda) - 0.00028 \text{ H}\right) \tag{7}$$

where ZHD depends on actual surface pressure Ps (hPa), on latitude λ (rad) and on the surface height H (km). The error introduced by the assumption of hydrostatic equilibrium in the model formulation is typically of the order of 0.01%, corresponding to 0.2 mm in the zenith delay.


$$\text{LIPV} \text{V} = \text{II} \times \text{ZVD} \tag{8}$$

Typical values for the parameter П are approximately 0.16, so 6 mm of ZWD is equivalent to about 1 mm of IPWV.

The parameter П is a function of various physical constants and of the weighted mean temperature Tm of the atmosphere (Askne & Nordius, 1987; Davis et al., 1985):

GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 177

The IPWV retrieval by means of a GNSS ground-based receiver can be used to monitor *in situ* water vapour time series, or to compare the IPWV values estimated by co-located ground-based sensors (e.g. microwave radiometer, photometer). Networks of GNSS receivers can be used to monitor the water vapour field, mapping its horizontal distribution. The possibility of mapping IPWV measured by GNSS networks has been explored (de Haan et al., 2009; Morland & Matzler, 2007), also combining IPWV data retrieved from GNSS receivers and from satellite-based radiometers to produce IPWV maps over extended areas

The degree of accuracy in IPWV estimation by GNSS receivers exploiting the tropospheric propagation delay at L-band is usually around 0.10-0.20 cm. The horizontal resolution of zenith columnar water vapour associated to a single receiver using standard methods (azimuthally symmetric weighting functions) is in the order of tens of kilometers, roughly corresponding to the aperture of the cone which includes all the lines of sight of the various

Besides GNSS, several techniques are well established to derive the vertically IPWV, such as ground-based microwave radiometers (MWR), radiosonde observations (RAOBs), analysis data from Numerical Weather Prediction Models (e.g ECMWF). Some examples of IPWV comparisons among different techniques during experimental campaigns are reported in

For instance, during an experimental campaign in Rome, Italy (20 September - 3 October, 2008), different instruments managed by the Sapienza University of Rome were operative at the same site: a GPS receiver (included in the Euref Permanent Network) a MWR (a dualchannel type, 23.8 and 31.4 GHz, model WVR-1100, Radiometrics) and six RAOBs (Pierdicca et al., 2009). Also, analysis data from ECMWF nearest the site were considered. The *IPWV*

Fig. 1. Rome, Sapienza University of Rome (41.89 N and 12.49 E, 72 m a.s.l.), 20 September - 3 October, 2008. Time series of IPWV from MWR (blue dots), GPS (green), RAOBs (yellow

(Basili et al., 2004; Lindenbergh et al, 2008).

GNSS satellites observed at different elevation angles.

time series for the entire campaign are plotted in Fig. 1.

squares) and ECMWF (magenta circles).

**2.3 Results** 

this sub-section.

$$T\_m = \frac{\int (e \, / \, T) dz}{\int (e \, / \, T^2) dz} \tag{9}$$

$$
\Pi = 10^6 \Big/ \rho R\_v \left[ \left( k\_3 \, / \, T\_m \right) + \left( k\_2 - m k\_1 \right) \right] \tag{10}
$$

where ρ is the density of liquid water, Rν is the specific gas constant for water vapour, m is the ratio of molar masses of water vapour and dry air, and k1, k2, k3 are the constants defined previously.

The transformation described in eq. 8 assumes that the wet path delay is entirely due to water vapour and that liquid water and ice do not contribute significantly to the wet delay (Duan et al., 1996).

#### **2.2 State of the art**

The '90s witnessed the fast increasing of the use of the tropospheric delay time of GNSS signals to estimate the Integrated Precipitable Water Vapour (Bevis et al., 1992; Bevis et al., 1994; Businger et al., 1996; Coster et al., 1997; Davies & Watson, 1998; Duan et al., 1996; Emardson et al., 1998; Kursinski, 1994; Rocken et al., 1993; Ware et al., 1997; Yuan et al., 1993).

Although the IPWV retrieval algorithm from ZTD measurements is well-established, different strategies were adopted for the time-varying parameter П*.* Anyway, П can be estimated with such an accuracy that very little uncertainty is introduced during the computation of eq. 8.

Bevis et al. (1994) provided an error budget for П and showed that in most practical conditions the uncertainty for this parameter is essentially due to the uncertainty for Tm (usually predicted from the surface temperature Ts on the basis of regressions), leading to a relative error in П of the order of 2%. In fact, exact calculations of Tm require profiles of atmospheric temperature and water vapor, as from radiosoundings or analysis from Numerical Weather Prediction Models (e.g the global European model, ECMWF). Since those data are not easily available, Tm is commonly estimated using station data of surface air temperature with empirical linear or more complicated relationship (the so-called Tm-Ts relationship) that can be site-dependent and may vary seasonally and diurnally (Bevis et al., 1994).

A simple and alternative approach can be considered for П estimation: the use of a linear regression (ZWD and IPWV as predictors and predictands, respectively) from historical data base of radiosoundings or ECMWF available near the site of interest for the water vapour estimation, leading again to a relative error in П just above 2%. Considering monthly averages of П the uncertainty is around 1.5% (Basili et al., 2001). This approach does not need measurements of surface temperature for each computation of П.

Estimation of water vapour features by GNSS is valuable from the point of view of climate monitoring, atmospheric research, and other applications such as ground-based and satellite-based sensor calibration and validation. GNSS tropospheric delays are also useful for operational weather prediction models (Gutman & Benjamin, 2001; Macpherson et al., 2008; Smith et al., 2000).

The IPWV retrieval by means of a GNSS ground-based receiver can be used to monitor *in situ* water vapour time series, or to compare the IPWV values estimated by co-located ground-based sensors (e.g. microwave radiometer, photometer). Networks of GNSS receivers can be used to monitor the water vapour field, mapping its horizontal distribution.

The possibility of mapping IPWV measured by GNSS networks has been explored (de Haan et al., 2009; Morland & Matzler, 2007), also combining IPWV data retrieved from GNSS receivers and from satellite-based radiometers to produce IPWV maps over extended areas (Basili et al., 2004; Lindenbergh et al, 2008).
