Numerical Weather Model

5.2.2.1 Introduction

NMWs are three dimensional layered models of the atmospheric conditions from the surface of the Earth up to an altitude of about 30 km. The models contain meteorological and geographical parameters such as temperature, pressure, relative humidity and geopotential height. The primary use of NWMs is in the domain of weather prediction when paired with a dynamical model but in this study the interest is purely in the current meteorological state. Indeed, data extracted from these model are combined over 3 hours, assuming all observations occur at the midpoint [118] (therefore temporal variations are not captured over these 3 hours) and radars have an horizontal resolution of 15km but augmented with a wide variety of sensors (as shown in Figure 57) [119] that enables a higher resolution of the final NWM format. Accuracy of some atmospherical parameters are shown for Arome with vertical profiles in 5.2.2.2 in Figure 65, Figure 66 and Figure 67.

Two NWMs are used in this study: Harmonie [120] provided by KNMI (Royal Netherland Meteorological Institute) and Arome [121] provided by Meteo France. Both models are essentially the same (few physical parameterization differences exist and are neglected in this study).

5.2.2.2 Arome

One year (01/2014 - 12/2014) of Arome data with a resolution of 3 hours have been processed. The geographic limits shown in Figure 58 are defined by latitudes 44°19'49,5"N and 46°43'24,8"N and longitudes 5°11'57,4"E and 11°47'27,8"E with a horizontal grid resolution of 2.5km.

Figure 58-Area of study with Arome – Source : Google Earth V7.1.5.1557- 10/04/2013

Parameters available from this NWM are Pressure, Temperature and Relative Humidity for 12 height levels represented in Figure 60 (from 20 to 3000meters) and 15 Isobar levels (100hPa, 150hPa, 200hPa, 250hPa,

300hPa, 400hPa, 500hPa, 600hPa, 700hPa, 800hPa, 850hPa, 900hPa, 925hPa, 950hPa, 1000hPa). The surface heights of these data over the region are represented in the following Figure 59.

Figure 59-Surface height of Arome domain

The 12 Height levels Arome data represented in the Figure 60 (where 2 levels are below 200ft) can be used to validate the Tropospheric Correction as defined in standards [16] [84] and to assess the duct issue (vertical abnormal behavior below the Aircraft).

The Isobar levels could be used for computing the total range tropospheric delay along the path from ground to satellites because these levels will be defined for higher heights than for the 12 heights levels.

These data, extracted from these isobar levels can be represented in the vertical plane as a function of longitude with a constant latitude (or as a function of latitude with a constant longitude). Parameters are represented through the following figures: heights on Figure 61, pressures on Figure 62, temperatures on Figure 63 and finally relative humidities on Figure 64 . In each figure, the black lines represent values given for the surface level then levels increase until the top of the grid (16km) starting from lines in the “warmest” colors (red) to the lines in “coldest” colors (blue).

Figure 61-Height levels of NWM

Figure 63-Temperature levels of NWM

In this last Figure 63 where each level of temperatures are represented, it is noted that it could appear that for some longitudes (as 9° for instance), it exists temperature levels whose values are superior to the temperature at the surface height (represented by the black line). This could be seen as temperature inversion which is a potential cause of atmospherical phenomena such as ducts (introduced in 4.2.2.1.2).

Figure 64-RH levels for NWM

This Figure 64 representing the relative humidity levels is difficult to analyze but it could be noted that for levels closed to the surface (black and warmest color lines) RH values vary significantly with longitude whilst for the highest levels (in dark blue), these values seem more stable (smoothed). This could be explained by the fact that effectively the humidity is more stable at higher altitudes than close to the surface where clouds and weather instabilities are frequently present.

In order to judge the accuracy of parameters extracted from such Numerical Weather Model, Meteo France [118] provided vertical profiles (in Pressure coordinates (hPa)) of the average errors of atmospherical parameters over the 2014 year, computed by comparing the extracted analyzed data with radio-sonde observations. Heights, Temperature and Relative Humidity profiles are represented in the figures below. Error biases are represented by the dashed lines and Mean Square Errors (MSE) in solid lines.

Figure 65-Vertical Profiles (over pressure coordinates in hPa) for Height Parameter in meters

Figure 67-Vertical Profiles (over pressure coordinates in hPa) for RH Parameter in %

It could be relevant to add that according the discussion with Meteo France scientist [118], horizontal correlation between parameters in among 15km (i.e 50% of correlation is observed for higher distances than 15km). That means that in this PhD study context, by considering that the highest distance between the ground station and the aircraft at 200ft (Cat I decision height) with regards to the Ground Facility siting of 𝐷𝑇𝐻=5km (as defined in standards [117] ) is about 6.5km, the correlation between errors will be about 74%.

5.2.2.3 Harmonie

Two years (09/2012 - 09/2014) of Harmonie data with a resolution of 3 hours have been processed. The geographic limits shown in Figure 68 are defined by latitudes from 49.00 to 55.88 degrees and longitudes from 0.00 to 9.99 degrees with a horizontal grid resolution of 2.5km.

Figure 68-Harmonie domain –Source: Google Earth V7.1.5.1557- 10/04/2013

Parameters available from this NWM are: Surface Geopotential Height, Surface Pressure as surface parameters and also Temperature, Specific Humidity for 60 levels in the vertical, with the top level at 0.1 hPa. These parameters could be also represented as for Arome data for each levels as a function of longitudes or latitudes in a plane (Figure 61, Figure 62, Figure 63, Figure 64) but they won’t be shown in this report.

The Height of the surface over the Harmonie domain extracted from the data is represented on the Figure 69

Figure 69-Surface height of Harmonie domain

Once these atmospheric parameters obtained, the range tropospheric delay can be modelled and computed with different approaches. They are explained in the following sections 5.3.1, 5.3.2 and 5.3.3 of this report.