**2.3 Results**

176 Remote Sensing of Planet Earth

*T*

6

ρ

10

*Π*

defined previously.

(Duan et al., 1996).

**2.2 State of the art** 

computation of eq. 8.

2008; Smith et al., 2000).

1993).

2 (/ ) (/ ) *<sup>m</sup>*

3 21

[( / ) ( )] *v m*

(9)

*R k T k mk* <sup>=</sup> + − (10)

*e T dz*

*e T dz* <sup>=</sup>

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

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

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.,

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

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

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

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.,

site-dependent and may vary seasonally and diurnally (Bevis et al., 1994).

need measurements of surface temperature for each computation of П.

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 GNSS satellites observed at different elevation angles.

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 this sub-section.

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

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 squares) and ECMWF (magenta circles).

GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 179

published by Notarpietro et al. (2011), results obtained applying a tomographic inversion to real observations taken on October 2010 in Italy, by a dense network of GNSS receivers.

Several activities were carried out in the past in the field of neutral atmospheric tomography based on observations performed on GNSS signals. Starting from one of the first concept description given by Elosegui et al. (1999), the effectiveness of a 4-dimensional (4D) water vapour field tomographic reconstruction was assessed by Flores et al. (2000) on a 20x20x15 km atmospheric domain against ECMWF (European Centre for Medium-Range Weather Forecast) data. After that, several methods were applied to different kind of real or simulated GPS observables (obtained by more or less dense receiver networks), demonstrating the effectiveness of water vapour field reconstructions on different atmospheric volume sizes, with different resolutions, against radiosonde data, Numerical Weather Prediction models or other independent water vapour dataset. Some reference papers (the list is not exhaustive) are that of Hirahara (2000), Gradinarsky and Jarlemark (2004), Champollion (2005, 2009), Bi et al. (2006), Troller et al. (2006), Nilsson and

In the framework of the European Space Agency project METAWAVE (Mitigation of Electromagnetic Transmission errors induced by Atmospheric Water Vapour Effects), we applied a new approach to the ZWDs estimated from the observations collected by a local network of GPS geodetic receivers deployed over a small area around the city of Como. Such new approach is based on an algorithm previously developed, on which we shown, from a simulative point of view only, the possibility to infer wet refractivity fields without using first guess atmospheric models and without adopting any a priori informations (Notarpietro et al., 2008). Such an algorithm has been applied to real measurements collected by a local network

of GPS receivers. In what follows we will summarize the results we obtained.

**3.2 Theoretical basis, retrieval technique, observables and validation approach** 

wet 6

w

10 N *ds* <sup>−</sup> ΔΦ = (11)

ray-path

Basically, two different classes of algorithms can be applied to perform atmospheric tomography (and tomography in general). The first belongs to iterative reconstruction techniques (for example the Algebraic, the Multiplicative Algebraic or the Simultaneous Iterative Reconstruction Techniques, respectively called ART, MART and SIRT, see Herman 1980) which need a good first guess atmospheric model to converge at the "good" solution. The second belongs to the Least Square Inversion (or Generalized Inversion) techniques, which are "one-step" algorithms and do not need a first guess. Notarpietro et al. (2008), shown the possibility to infer Wet Refractivity fields without using first guess atmospheric models. The algorithm accomplishes the reconstruction in two consecutive steps. The first step allows the retrieval of a "raw" three dimensional wet refractivity distribution directly from Slant Wet Delays (SWD) observables ΔΦwet (defined as equivalent optical length), which in turn depend on the wet refractivity (Nw) distribution along the ray path, in the way

**3.1 State of the art** 

Gradinarsky (2006).

defined by the following equation:

The IPWV root mean square (rms) difference of GPS compared with MWR is 0.10 cm, with RAOBs and ECMWF is around 0.15 cm.

With reference to an Italian ground-based network of GPS receivers, managed by the Italian Space Agency (ASI), another experimental campaign was conducted in Cagliari (Italy), during the whole 1999 (Basili et al., 2001). The experimental site was selected at the Cagliari GPS station where a ground-based dual-channel microwave radiometer (WVR-1100) was operated for the whole campaign of measurements. Also, data from RAOBs released at Cagliari every six hours were available. Results of the experiment for the whole 1999 are shown in Fig. 2, gathered in non-precipitating conditions to avoid problems with the radiometer measurements. The comparison is performed considering a sampling time of 6 hours, in coincidence with RAOB releases.

This long-term comparison has shown a fairly good agreement among the two remote sensors and the RAOBs, with an error standard deviation similar to other experiments reported in literature.

Fig. 2. Scatterplots of IPWV computed at Cagliari, 1999, by three different instruments (RAOB, GPS and WVR). Left: IPWV-GPS vs. IPWV-RAOB; right: IPWV-WVR vs. IPWV-GPS (Basili et al. 2001). Bias and STD refer to the mean difference and to the standard deviation of the difference.

## **3. Wet atmospheric refractivity maps through tomography**

As it has already been shown in Section 2, the remote sensing of "wet" troposphere is possible by estimating the wet contribution to atmospheric total delay mapped into the zenith direction, the ZWD, in the general adjustment of double difference phase observations. Following a step ahead, it is also possible to try to extract some information on the three dimensional distribution of atmospheric parameters, from total delay observations taken by different line of sights. Tomography deals with the inversion of integral measurements collected from a great variety of directions, for the extraction of nonhomogeneous signatures inside the analyzed volume. Requirements necessary to make tomographic inversion procedures effective are well known. The geometry of the signal paths is crucial for the stability of the inversion procedure. All the voxels (volume pixels) have to be crossed by a lot of rays coming from different directions. Horizontal resolution can be improved only considering quite dense GNSS networks. Vertical resolution can be improved if receivers are deployed on a sloped area. This section presents results already published by Notarpietro et al. (2011), results obtained applying a tomographic inversion to real observations taken on October 2010 in Italy, by a dense network of GNSS receivers.

#### **3.1 State of the art**

178 Remote Sensing of Planet Earth

The IPWV root mean square (rms) difference of GPS compared with MWR is 0.10 cm, with

With reference to an Italian ground-based network of GPS receivers, managed by the Italian Space Agency (ASI), another experimental campaign was conducted in Cagliari (Italy), during the whole 1999 (Basili et al., 2001). The experimental site was selected at the Cagliari GPS station where a ground-based dual-channel microwave radiometer (WVR-1100) was operated for the whole campaign of measurements. Also, data from RAOBs released at Cagliari every six hours were available. Results of the experiment for the whole 1999 are shown in Fig. 2, gathered in non-precipitating conditions to avoid problems with the radiometer measurements. The comparison is performed considering a sampling time of 6

This long-term comparison has shown a fairly good agreement among the two remote sensors and the RAOBs, with an error standard deviation similar to other experiments

Fig. 2. Scatterplots of IPWV computed at Cagliari, 1999, by three different instruments (RAOB, GPS and WVR). Left: IPWV-GPS vs. IPWV-RAOB; right: IPWV-WVR vs. IPWV-GPS (Basili et al. 2001). Bias and STD refer to the mean difference and to the standard deviation

As it has already been shown in Section 2, the remote sensing of "wet" troposphere is possible by estimating the wet contribution to atmospheric total delay mapped into the zenith direction, the ZWD, in the general adjustment of double difference phase observations. Following a step ahead, it is also possible to try to extract some information on the three dimensional distribution of atmospheric parameters, from total delay observations taken by different line of sights. Tomography deals with the inversion of integral measurements collected from a great variety of directions, for the extraction of nonhomogeneous signatures inside the analyzed volume. Requirements necessary to make tomographic inversion procedures effective are well known. The geometry of the signal paths is crucial for the stability of the inversion procedure. All the voxels (volume pixels) have to be crossed by a lot of rays coming from different directions. Horizontal resolution can be improved only considering quite dense GNSS networks. Vertical resolution can be improved if receivers are deployed on a sloped area. This section presents results already

**3. Wet atmospheric refractivity maps through tomography** 

RAOBs and ECMWF is around 0.15 cm.

hours, in coincidence with RAOB releases.

reported in literature.

of the difference.

Several activities were carried out in the past in the field of neutral atmospheric tomography based on observations performed on GNSS signals. Starting from one of the first concept description given by Elosegui et al. (1999), the effectiveness of a 4-dimensional (4D) water vapour field tomographic reconstruction was assessed by Flores et al. (2000) on a 20x20x15 km atmospheric domain against ECMWF (European Centre for Medium-Range Weather Forecast) data. After that, several methods were applied to different kind of real or simulated GPS observables (obtained by more or less dense receiver networks), demonstrating the effectiveness of water vapour field reconstructions on different atmospheric volume sizes, with different resolutions, against radiosonde data, Numerical Weather Prediction models or other independent water vapour dataset. Some reference papers (the list is not exhaustive) are that of Hirahara (2000), Gradinarsky and Jarlemark (2004), Champollion (2005, 2009), Bi et al. (2006), Troller et al. (2006), Nilsson and Gradinarsky (2006).

In the framework of the European Space Agency project METAWAVE (Mitigation of Electromagnetic Transmission errors induced by Atmospheric Water Vapour Effects), we applied a new approach to the ZWDs estimated from the observations collected by a local network of GPS geodetic receivers deployed over a small area around the city of Como. Such new approach is based on an algorithm previously developed, on which we shown, from a simulative point of view only, the possibility to infer wet refractivity fields without using first guess atmospheric models and without adopting any a priori informations (Notarpietro et al., 2008). Such an algorithm has been applied to real measurements collected by a local network of GPS receivers. In what follows we will summarize the results we obtained.

#### **3.2 Theoretical basis, retrieval technique, observables and validation approach**

Basically, two different classes of algorithms can be applied to perform atmospheric tomography (and tomography in general). The first belongs to iterative reconstruction techniques (for example the Algebraic, the Multiplicative Algebraic or the Simultaneous Iterative Reconstruction Techniques, respectively called ART, MART and SIRT, see Herman 1980) which need a good first guess atmospheric model to converge at the "good" solution. The second belongs to the Least Square Inversion (or Generalized Inversion) techniques, which are "one-step" algorithms and do not need a first guess. Notarpietro et al. (2008), shown the possibility to infer Wet Refractivity fields without using first guess atmospheric models. The algorithm accomplishes the reconstruction in two consecutive steps. The first step allows the retrieval of a "raw" three dimensional wet refractivity distribution directly from Slant Wet Delays (SWD) observables ΔΦwet (defined as equivalent optical length), which in turn depend on the wet refractivity (Nw) distribution along the ray path, in the way defined by the following equation:

$$
\Delta\Phi^{\rm wet} = 10^{-6} \int\_{\rm ray\text{-path}} \mathbf{N}\_{\rm w} ds \tag{11}
$$

GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 181

Fig. 3. Geographic distribution of the MisT network. The two "mountainous" GPS receivers

A daily multi-station adjustment of observations collected by the whole network was performed via the Bernese V0.5 software, to estimate jointly the station positions and the Hourly ZWDs parameters. These are basically averaged value of the tropospheric delay zenithal projection, affecting all the signals from the considered station to all the satellites in view, as they move along their orbits in 1 h time. Differences between the actual instantaneous slant delays and these averaged values projected back on the slant direction are to be found in the double difference adjustment residuals (this analysis is not described here). More precisely, carrier phase double differences were processed, all the single differences being formed with respect to the COMO reference station. The Bernese software models the tropospheric delay in each station-receiver phase measurement as the sum of a hydrostatic component and a wet one. The first can be modelled (and slanted toward the satellite position using the dry Niell's mapping function (Niell, 1996)) considering the Saastamoinen formulation (Davis et al., 1985) and interpolating surface pressure data (in time and space) obtained by 0.25°x0.25° ECMWF analysis. The second can be expressed as the product of an unknown parameter, the ZWD, by a known coefficient computed in our case from the wet Niell's mapping function. For each MisT station, input data were Hourly ZWDs, estimated during the week from October 12th to October 18th, 2008 and from November 13th to November 19th, 2008. Hourly ZWDs related to each MisT station, were then "geometrically" projected along the slant paths (using Niell's mapping functions) by upsampling at 1-min sample intervals the 15 min GPS satellites positions obtained from International GNSS Service (IGS) sp3 files and inverted using the developed tomographic

It has to be pointed out that the standard dataset adopted for tomographic reconstructions is built up by considering only 6 out of 9 MisT receivers. Firstly, COMO, ANZA and CAST are the three stations belonging to the so called MisT inner sub-network. We considered only ANZA among the three close stations of COMO, ANZA and CAST (deployed at distances less than 200 m from one-another), whose ZWDs are highly correlated (>95%). Moreover, ZWD data obtained processing NAND observations are

are highlighted. The final volume discretization is also superimposed.

procedure.

Linearizing eq. 11 and considering the entire observation dataset, the following matrix equation turns out:

$$
\Delta \boldsymbol{\Phi}^{\text{wet}} = 10^{-6} \mathbf{L} \cdot \mathbf{N}\_{\text{w}} \tag{12}
$$

where **L** is the Data Kernel to be inverted to obtain the wet refractivity distribution, which is a matrix containing for each row, the lengths of each segment inside each voxel crossed by the generic rectilinear ray-path connecting the receiver and the satellite. This tomographic pre-processing step pertains to Least Square Inversion algorithms (Lawson & Hanson, 1974). It achieves the result through the constrained inversion (using Singular Value Decomposition) of the Tikonov-regularized Data Kernel matrix. Although the resolution obtainable with this pre-processing step is quite rough (the entire tropospheric volume has been divided into 2x2x20 voxels grid), this result is used as first guess for the algebraic technique used in the second phase of the proposed reconstruction algorithm. In particular we applied the SIRT technique to obtain the distribution of wet refractivity inside the tropospheric volume characterized by the final resolution (4x4x20 voxels grid).

With the aim of studying the potentialities of GNSS in the determination of local wet refractivity fields, needed for instance to correct InSAR derived landslide deformation maps, we used observations collected during a couple of weeks in 2008 by the MisT GPS network, defined by eight geodetic receivers that were deployed around the COMO Permanent Network station (which is placed in the North West part of Italy). This network was born for different purposes from the tomographic reconstruction of the wet refractivity field, and its design was not fully compliant with the requirements of this technique (details about each MisT station are reported in Table 1, while the MisT network topology is shown in Fig. 3). An attempt to improve the original design of the MisT network was done by performing a different daily campaign collecting data by two additional GPS portable receivers, named BISB and BOLE, placed at higher altitudes from the original network (respectively in the top of Monte Bisbino e Monte Boletto).


Table 1. MisT GPS network description. Highligthed raws are those related the two "mountainous" receivers

Linearizing eq. 11 and considering the entire observation dataset, the following matrix

where **L** is the Data Kernel to be inverted to obtain the wet refractivity distribution, which is a matrix containing for each row, the lengths of each segment inside each voxel crossed by the generic rectilinear ray-path connecting the receiver and the satellite. This tomographic pre-processing step pertains to Least Square Inversion algorithms (Lawson & Hanson, 1974). It achieves the result through the constrained inversion (using Singular Value Decomposition) of the Tikonov-regularized Data Kernel matrix. Although the resolution obtainable with this pre-processing step is quite rough (the entire tropospheric volume has been divided into 2x2x20 voxels grid), this result is used as first guess for the algebraic technique used in the second phase of the proposed reconstruction algorithm. In particular we applied the SIRT technique to obtain the distribution of wet refractivity inside the

With the aim of studying the potentialities of GNSS in the determination of local wet refractivity fields, needed for instance to correct InSAR derived landslide deformation maps, we used observations collected during a couple of weeks in 2008 by the MisT GPS network, defined by eight geodetic receivers that were deployed around the COMO Permanent Network station (which is placed in the North West part of Italy). This network was born for different purposes from the tomographic reconstruction of the wet refractivity field, and its design was not fully compliant with the requirements of this technique (details about each MisT station are reported in Table 1, while the MisT network topology is shown in Fig. 3). An attempt to improve the original design of the MisT network was done by performing a different daily campaign collecting data by two additional GPS portable receivers, named BISB and BOLE, placed at higher altitudes from the original network (respectively in the top

Station Height Receiver type ANZA 280 m Leica GRX1200 BRUN 738 m Leica GX1200 CAST 286 m Leica GRX1200 COMO 292 m Topcon Odyssey LAPR 349 m Leica GX1200 PRCO 266 m Leica GX1200 NAND 746 m Leica GX1200 MGRA 353 m Leica GX1200 DANI 614 m Leica GX1200 BISB 1373 m Topcon GB1000 BOLE 1199 m Trimble 4700 Table 1. MisT GPS network description. Highligthed raws are those related the two

tropospheric volume characterized by the final resolution (4x4x20 voxels grid).

<sup>6</sup> <sup>10</sup><sup>−</sup> = ⋅ **wet ΔΦ L Nw** (12)

equation turns out:

of Monte Bisbino e Monte Boletto).

"mountainous" receivers

Fig. 3. Geographic distribution of the MisT network. The two "mountainous" GPS receivers are highlighted. The final volume discretization is also superimposed.

A daily multi-station adjustment of observations collected by the whole network was performed via the Bernese V0.5 software, to estimate jointly the station positions and the Hourly ZWDs parameters. These are basically averaged value of the tropospheric delay zenithal projection, affecting all the signals from the considered station to all the satellites in view, as they move along their orbits in 1 h time. Differences between the actual instantaneous slant delays and these averaged values projected back on the slant direction are to be found in the double difference adjustment residuals (this analysis is not described here). More precisely, carrier phase double differences were processed, all the single differences being formed with respect to the COMO reference station. The Bernese software models the tropospheric delay in each station-receiver phase measurement as the sum of a hydrostatic component and a wet one. The first can be modelled (and slanted toward the satellite position using the dry Niell's mapping function (Niell, 1996)) considering the Saastamoinen formulation (Davis et al., 1985) and interpolating surface pressure data (in time and space) obtained by 0.25°x0.25° ECMWF analysis. The second can be expressed as the product of an unknown parameter, the ZWD, by a known coefficient computed in our case from the wet Niell's mapping function. For each MisT station, input data were Hourly ZWDs, estimated during the week from October 12th to October 18th, 2008 and from November 13th to November 19th, 2008. Hourly ZWDs related to each MisT station, were then "geometrically" projected along the slant paths (using Niell's mapping functions) by upsampling at 1-min sample intervals the 15 min GPS satellites positions obtained from International GNSS Service (IGS) sp3 files and inverted using the developed tomographic procedure.

It has to be pointed out that the standard dataset adopted for tomographic reconstructions is built up by considering only 6 out of 9 MisT receivers. Firstly, COMO, ANZA and CAST are the three stations belonging to the so called MisT inner sub-network. We considered only ANZA among the three close stations of COMO, ANZA and CAST (deployed at distances less than 200 m from one-another), whose ZWDs are highly correlated (>95%). Moreover, ZWD data obtained processing NAND observations are

GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 183

Fig. 4. Time series of ZWDs measured (blue dots) and estimated (red dots) after

Table 2. Statistics of the ZWD difference (measured-estimated after reconstruction) over the

Considering the baseline scenario described in paragraph 3.3.1, it is clear that the improvement in the reconstruction of lower layers is strictly related to the availability of trajectories crossing (and discriminating) the lower tropospheric layers. In our tomographic reconstruction, only rays exiting from the top boundary of the analyzed 18x26 km2x10 km volume were considered. In our case, the mean elevation angle was about 30°. Since the MisT network topography is fixed, to overcome this limit and therefore improving the retrieved field, we try to ingest also low elevation trajectories which enter from the lateral boundaries of the analyzed volume. Since SWDs associated to these rays contains both a contribution of the wet refractivity field inside the considered volume (namely, the inner volume) and outside the volume (the outer volume) up to 10 km height, we modelled and removed this last quantity from the SWDs associated to low elevation (< 30°) ray before entering the tomographic approach. The wet refractivity model considered in the outer

a. from a very coarse tomographic reconstruction performed on a bigger volume using the same GNSS experimental data (considering as input data those observed by the entire

b. interpolating the CIRA-Q wet atmospheric climatologic model (Kirchengast et al., 1999)

c. considering data taken by ECMWF analysis (91 pressure levels, 0.25°x0.25° grid resolution), collocated in time and space with the centre of each voxel belongs to the

reconstruction above NAND station, for the baseline experiment.

NAND reference station.

in the outer volume;

**3.3.2 Ingestion of low elevation observations** 

volume was obtained considering three different approaches:

MisT network except those taken by the NAND receiver);

used for self-consistency validation purposes ('leave-one-out' quality assessment) and are not included in the input dataset.

As we have previously stated, our tomographic approach is based on two consecutive reconstruction steps. The first one (data kernel generalized inversion) creates the first guess field for the second one (algebraic tomography), which doubles the horizontal resolution (from 2x2x20 to a 4x4x20 voxels grid, i.e. means 4.5x6.5x0.5 km3). It has to be stressed that volume resolution is strictly related to the geometrical distribution of GNSS receivers and to the availability of observations. Higher resolutions would introduce an increasing number of voxels not crossed by any ray, thus worsening the final results. On the contrary, lower resolutions would imply a too coarse description of the field.

Considering the available observables we were able to obtain 168 or 144 Hourly wet refractivity maps (for the October or the November week respectively). Validation is carried out considering the difference between ZWD GNSS measurements taken over NAND receiver and corresponding ZWD estimates evaluated by vertically integrating the reconstructed wet refractivity maps. Considering the entire observing period, final statistics are thus based on 168 (144) ZWD differences (measured-estimated) distribution for the October (November) week and results are given in terms of their mean values and their rms values.
