Tropospheric Correction Analysis

This part of the report assesses the tropospheric correction and the vertical anomalies which can be caused by tropospheric ducts. First some results found in literature are presented, then a real data analysis is performed and results found by using NWM data are given.

5.5.2.1 Literature Results

Previous investigations have analyzed the presence of tropospheric ducts. Particularly in [129] , a description of tropospheric ducts is given and some results are presented. Indeed, it appears that these vertical anomalies can cause errors of up to 7cm with a high likelihood of occurrence. Then, a threat model is derived for establishing a duct threat model in the form of ranging measurement error probability distribution. The corresponding histogram shows that the maximum error observed at 200m is 6mm in zenith (5cm for a 7°elevation satellite signal) and that the duct error distribution is non Gaussian and is non-zero mean. These literature [129] suggests that these duct errors cannot simply be accounted for by inflating the measurement standard deviation and methods such as bounding ranging biases approach and inflation approach (as detailed in Chapter Chapter 6) are proposed.

5.5.2.2 Numerical Weather Model Based Results

In this section, Arome (5.2.2.2) data and Harmonie (5.2.2.3) data are analyzed and compared to assess the tropospheric correction and the possible ducts. Indeed, according literature [129] and some discussions with specialists [130], ducts tend to form when some abnormal behavior and sudden change concerning temperature (increasing with height) or/and relative humidity appear. Therefore ducts should be more important and should occur more frequently in mountain area such in Arome area (Alpines data) but for comparison purpose, results obtained in Alpines data are compared to those of Harmonie.

Furthermore, some studies about vertical gradients within the Harmonie data were already undertaken by NLR [105]during the SESAR project investigations dealing with the WP15.3.7.

Then three locations were investigated: Turin Airport, Milan with the Arome data and Schiphol with the Harmonie data.

Longitude(°) Latitude(°) Height(m)

Turin 7.382185 45.005447 316.6

Milan 9.1881714 45.463681 103

Schiphol 4.7642 52.3080 -3

In the Zenith Direction, the tropospheric correction and the standard deviation of the residual tropospheric error computed as explained in 3.2.3.3.2.1 and 3.2.3.3.2.2 are summarized in the Table 25:

TC(m) (m)

Turin 0.0178 0.0023

Milan 0.0129 0.0016

Schiphol 0.0195 0.00057

Table 25-TC and sigma tropo for Turin, Milan and Schiphol locations

In order to evaluate how the user is protected during an approach (20NM (37km) for the farthest point along the approach path), for each of these three locations a “squared-subgrid” with a 80km length horizontally and vertically was selected in order to cover both sides of each location approach. Then statistical analysis is performed over 1year of data (from the 1st _{January 2014 at 00h00) for each locations over its corresponding}

subgrid.

First for each location, difference between the zenith tropospheric delay and the zenith TC over these subgrids were computed and plotted in the following figures respectively for Turin, Milan and Schiphol:

Figure 96-Difference between TC and ZTD for Turin

By analyzing this Turin case in the Figure 96, errors between TC and ZTD are at one centimeter level and the variation within this grid is up to 1mm.

Figure 97-Difference between TC and ZTD for Milan

Concerning the Milan location case in the Figure 97, errors between TC and ZTD are up to 8.5millimeters and the variation within this grid is up to 2mm. Therefore with this 2mm level, error variations appear more important at this location compared to Turin location where 1mm level variation was observed.

Figure 98-Difference between TC and ZTD for Schiphol

For the Schiphol location case in the Figure 98, errors between TC and ZTD are up to 1.2centimeters and the variation within this grid is up to 0.5mm. By comparing this variation level with other cases above, error variations appear less important at this location compared to Milan and Turin location where 2mm and 1mm level variations were observed respectively. This conclusion could be expected by guessing that in Alpines area, weather variations should be more important than in a flat domain such as Netherlands.

Then the mean errors between the zenith tropospheric delay and the zenith tropospheric correction over these subgrids were computed and it appears that the standards deviations for these errors over the grid is really small compared to the 𝜎𝑡𝑟𝑜𝑝𝑜given in the previous Table 25 as the following figures show:

Figure 99-STD of (TC-ZTD) over the grid compared to sigma tropo at Turin

Figure 101-STD of (TC-ZTD) over the grid compared to sigma tropo at Schiphol

By analyzing these figures, because the standard deviation of the error between ZTD and TC all over the grid can be considered as small compared to the 𝜎𝑡𝑟𝑜𝑝𝑜 for each location, it could be concluded that the spatial variation is not important for this statistical study and the analysis realized at one location can lead to same conclusions as for all the grid without a huge impact. That is why for the following work of this statistical analysis, only Turin, Milan and Schiphol locations are investigated.

Therefore, differences between TC and ZTD were computed over all epoch for each NWM (1 year for Arome, 2 years for Harmonie) at Turin, Milan and Schiphol. Then histograms were realized in order to analyze the errors distribution at these locations and they are represented below:

Figure 103-Histogram of TC-ZTD over 1 year at Milan

Figure 104-Histogram of TC-ZTD over 2 years at Schiphol

By viewing these distributions of the errors between TC and ZTD, it can be remark that they are not centered and biases appear which are not covered by the actual TC computation. (Note that these histograms of Turin, Milan and Schiphol have respectively a resolution of 0.04mm, 0.022mm and 0.02mm).

Indeed, the following table represents these ranging biases named 𝜇𝑇𝐶 for each location. They were obtained by taking the mean of the distributions illustrated by previous histogram. It could be considered as an approximation of the bias because they could not have enough samples in the study to represent this non- stationary processus.

Turin 0.0118

Milan 0.0086

Schiphol 0.0114

Table 26-Bias between TC and ZTD

By analyzing the previous table, ranging biases are not negligible and have to be treated. Indeed, in the slant domain they can lead to higher values (up to 12cm) than those presented in zenith direction by this previous table as represented in the following figure:

Figure 105-TC bias

Two possibilities can be applied for dealing with them. Either, the TC computation have to be modified. These methodology was already suggested and studied by NLR into the SESAR project [105]. Or these ranging biases have to be bound as the same way as for non-nominal troposphere explained and illustrated in Chapter 6 and included in the VPL computation.

Also, the amplitude of deviation from the mean values 𝜇𝑇𝐶 of these histograms Figure 102, Figure 103 and Figure 104 can reach 2mm in zenith. Therefore, because the errors due to mismodelling are included in the bias term 𝜇𝑇𝐶, this deviation can be the effect of duct phenomena as observed in literature and shown in 5.5.1.1. Further work needs to be done for assessing properly the presence of these vertical anomalies as mentioned in 7.2.

Indeed, as presented in 5.5.2.1, ducts tend to form when some abnormal behavior and sudden changes of temperature variation with height (increasing with height) or/and relative humidity appear. Therefore, refractivity will not follow the typical nominal curve (as shown in Figure 76 and in literature [129]), that is why it is possible to compare the results obtained through the tropospheric correction analysis (5.5.2) with the behavior of the refractivities.

The same methodology as explained in [129] was applied for the worst set of data found in the statistical analysis in 5.5.2.2. Therefore refractivities where computed and plotted during the assumed duct phenomena and compared to the nominal trend of refractivities. Indeed, it was assumed that refractivity gradient under nominal conditions is about -40/km. The following figure was obtained.

Then for computing the differential tropospheric delay, the area between the two curves was determined and value obtained was about 0.033mm which is really small compared to value found during ducting phenomena in [129]. Therefore, it could be concluded that this deviation observed in 5.5.2.2. seems to be not due to duct

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5.5.3 Conclusions

In this subsection dealing with vertical component of the differential range tropospheric delay, the overbounding Gaussian model for the TC error which had been previously validated for nominal and rare conditions [84] [16] was presented. Then the NWMs data was used to compute to derive values of TC and 𝜎𝑡𝑟𝑜𝑝𝑜 for different locations.

To complete this study some investigations and statistical analysis with Arome (5.2.2.2) data and Harmonie (5.2.2.3) data were realized for analyzing the tropospheric correction. By seeing that the spatial variation of the error between ZTD and TC is not important for this statistical study, only locations such as Turin, Milan and Schiphol were investigated. Then after having analyzed distributions of their errors between TC and ZTD, it was remarked that they were not centered and ranging biases 𝜇𝑇𝐶 appeared which are not covered by the actual TC computation. These biases, in the slant domain, can lead to high values up to 12cm so they are not negligible and have to be treated. Therefore either, the TC computation have to be modified as it was already suggested and studied by NLR into the SESAR project [108]. Or these ranging biases have to be bound as the same way as for non-nominal troposphere explained in Chapter 6 and included in the VPL computation. Then, further work needs to be done for assessing properly the presence of vertical anomalies known as ducts as mentioned in 7.2. Preliminary analysis shown in 5.5.2.2 showed that this deviation is not due to ducts.

This section explained how to model the range troposphere delay within GBAS and how to estimate the worst differential range troposphere delay in order to model the anomalous troposphere. Then the following chapter Chapter 6 will presents some methodologies to bound this anomalous troposphere in order to protect the aircraft against these gradients.

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