**3.3.1 Baseline scenario results and effect of mountainous observation ingestion**

The baseline scenario is that defined considering observations taken by the reduced MisT network formed by ANZA, BRUN, LAPR, PRCO, MGRA and DANI stations. For the October week, tomographic reconstructions were carried out considering ZWDs observed by the reduced MisT network observations taken during 12–18 October. The good agreement between measured and estimated ZWD time series evaluated above NAND during this period and for this scenario is shown in Fig. 4, while some statistics are given in column A of Table 2. Since data from the two mountainous receivers (BISB and BOLE in Fig. 3) were available only on 12th October, 2008, between 9.00 am and 7.00 pm, comparisons of measured and estimated ZWDs above NAND receiver were performed also considering observations taken by the reduced MisT network in this smaller period (column B of Table 2). A bias decrease of 0.4 mm is observed adding BOLE (1199 m a.s.l.) observations (see column C, Table 2) and of 1 mm adding both BOLE and BISB (1373 m a.s.l.) data (see column D, Table 2) in the input dataset. This demonstrate the necessity of measurements collected at higher altitudes which allows a best reconstruction of vertical refractivity gradients characterizing the first three atmospheric layers. The high rms error with respect the one characterizing the baseline result given in column B, Table 2, is probably due to the more noisy data acquired by the two portable mountainous receivers (this is also evidenced by the decrease in correlation observed between NAND ZWDs measurements and estimates).

used for self-consistency validation purposes ('leave-one-out' quality assessment) and are

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

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

In what follows, we will show results related to the so called baseline scenario and improvements obtained adding observations taken by mountainous receivers and from low elevation angles. Some hints about the impact of distance and height of the reconstruction

The baseline scenario is that defined considering observations taken by the reduced MisT network formed by ANZA, BRUN, LAPR, PRCO, MGRA and DANI stations. For the October week, tomographic reconstructions were carried out considering ZWDs observed by the reduced MisT network observations taken during 12–18 October. The good agreement between measured and estimated ZWD time series evaluated above NAND during this period and for this scenario is shown in Fig. 4, while some statistics are given in column A of Table 2. Since data from the two mountainous receivers (BISB and BOLE in Fig. 3) were available only on 12th October, 2008, between 9.00 am and 7.00 pm, comparisons of measured and estimated ZWDs above NAND receiver were performed also considering observations taken by the reduced MisT network in this smaller period (column B of Table 2). A bias decrease of 0.4 mm is observed adding BOLE (1199 m a.s.l.) observations (see column C, Table 2) and of 1 mm adding both BOLE and BISB (1373 m a.s.l.) data (see column D, Table 2) in the input dataset. This demonstrate the necessity of measurements collected at higher altitudes which allows a best reconstruction of vertical refractivity gradients characterizing the first three atmospheric layers. The high rms error with respect the one characterizing the baseline result given in column B, Table 2, is probably due to the more noisy data acquired by the two portable mountainous receivers (this is also evidenced by the decrease in correlation observed between NAND ZWDs

**3.3.1 Baseline scenario results and effect of mountainous observation ingestion** 

error and about validation against independent data will be also given.

not included in the input dataset.

values.

**3.3 Results** 

measurements and estimates).

resolutions would imply a too coarse description of the field.

Fig. 4. Time series of ZWDs measured (blue dots) and estimated (red dots) after reconstruction above NAND station, for the baseline experiment.


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

#### **3.3.2 Ingestion of low elevation observations**

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 volume was obtained considering three different approaches:


GNSS Signals: A Powerful Source for Atmosphere and Earth's Surface Monitoring 185

(only 10 Hourly averaged ZWDs or ZTDs observations are contemporaneously available to

Fig. 5. rms of the differences between ZWDs (blue dots) or ZTDs (red dots) observed and estimated above each reference receiver, excluding data of that receiver from the input dataset before the reconstruction. All data observed by the MisT network during the entire week are taken into account. (Left) rms are plotted against the distance of the reference receiver from COMO master station. (Right) rms are plotted against the height of the reference receiver above WGS84. The degraded results obtained excluding BRUN receiver

Fig. 6. Like Fig. 5, but considering all data observed by the MisT network and by the two

First of all this analysis confirms the impact of a good height displacement of receivers in the network. Even if MisT network topography has not been optimized for the geography of the analyzed area and for tomographic applications, if we consider the impact of height in the evaluation of propagation delays, we can say that the lack of receivers placed at higher altitudes will worsen final results. In particular, considering the original MisT network, where all the receivers are more or less placed in the same layer of the map (Fig. 5) we want to highlight that, if data observed at the highest receiver (namely BISB, which is placed in another vertical layer) are not given in input to the tomography, the rms of the difference between estimated and measured zenith delays (both Wet and Total) is

mountainous receivers during the 10 hours of 12th October, 2008.

(which is the highest one) are highlighted.

generally doubled.

any receivers of the "extended" network). In this case results are shown in Fig. 6.

outer volume (this was done by a bilinear space interpolation and a linear time interpolation of the meteorological data).

Results related to this analysis are summarized in Table 3. They confirm the importance of the availability of low elevation measurements issued from different altitudes to improve the estimation of vertical refractivity gradients in such a tomographic approach. It has to be noted that the availability of external independent information (atmospheric models or, better, meteorological data) for modelling the SWD component of low elevation observations in the outer volume seems to be necessary in this case. Because of the MisT network design (receivers not homogeneously distributed in the inner volume), the internal procedure based on the coarse tomographic reconstruction (case a)) is not very effective.


Table 3. Self-consistency results considering SWD derived by low elevation observations (taken during the October week) after the application of the outer volume wet refractivity modelling strategies a., b. and c.. Results are relative to the statistics of ZWD errors (measured-estimated after reconstruction) over the NAND reference station. Results related to the baseline scenario are reported in the first column as a reference. In the last column the evident outliers due to measurements (see blue dots in Fig. 4) were removed.
