Wind model

Figure 4.20: Mean, maximum and 95 percentile dew point temperatures of Andoya as a function of the altitude.

4. Planetary thermal environment for stratospheric balloon thermal design 75

density above that altitude makes the Reynolds number, Re, decrease to values which make the forced convection less important with regard to the radiative heat transfer.

The main objective of wind data treatment is to derive a map with data sufficiently representative of the geographical region and the season of interest.

The information provided by this map will be used as the worst-case scenario in the thermal analyses in order to quantify the maximum convective heat transfer during the ascent phase in this kind of mission. Since the process followed to treat these data statistically is not straightforward, it is presented in the scheme shown in Figure 4.21 to clarify the procedure.

Figure 4.21: Scheme of the process followed to treat wind data statistically.

As said before, data retrieved from ESRAD are used for the analysis. When starting with processing wind velocity data, some wrong measurements too far from the mean of each day were found. In order to avoid its influence, original values with a percentile of 95 have been established as the starting point for the data

processing for each altitude resolution (75, 150 and 600 m). As an example, the heatmaps resulting after this first step are shown in Figure 4.22a for June 1^st, 2016.

Due to the different modes of the antenna, wind samples have different sampling times. As the goal is to obtain a combined map, every mesh has to be reshaped in order to homogenise every sampling time. These reshaped heatmaps for each altitude resolution are shown in Figure 4.22b for June 1^st, 2016.

(a) (b)

Figure 4.22: Original (a) and resampled (b) representation of the wind velocities for the 1^st June of 2016 for altitude resolutions of 75 m (upper row), 150 m (middle row) and 600 m (lower row).

Once every sample has the same mesh, it is possible to study the differences between the radar observation modes. Comparing values measured in every point by each mode, it is possible to establish a correlation between them. This can be observed when representing each pair of the trio, as is shown in Figure 4.23.

4. Planetary thermal environment for stratospheric balloon thermal design 77

Figure 4.23: Data correlation between each pair of radar modes corresponding to a complete day.

Moreover, the probability density function of each mode has been represented in the main diagonal for data corresponding to the 1^st June of 2016.

As can be observed in the graphs, a relationship can be established between different modes values. If both measured data were the same at each altitude and time, points should be found in a line of slope 1. However, paired data do not fit. The mean values of these three different data sets has been considered as the most probable scenario since they are measuring the same phenomena. By this way, the map shown in Figure 4.24a is obtained.

Even having combined three measurements corresponding with each altitude resolution, there are some missing values and some values too deviated from the mean distribution. Values out of the interval mean ± 2σ at each altitude have been discarded. The results are shown in Figure 4.24b.

In order to fill the voids on the map, a k-nearest neighbor (KNN) missing value imputation algorithm [81] has been implemented. This method consists in the imputation of a value to a point in a mesh using the values of the k nearest neighbors. In this case, k has been considered to be 4 and the mean value of thosek- neighbors has been assigned obtaining the map shown in Figure 4.25. To do so, both dimensions have been normalized in order to obtain the nearest values in the map.

(a) (b)

Figure 4.24: (a) Mean combination of every resolution measurement for the 1^st June of 2016, (b) Map after deletion of values out of the mean±2σ.

Figure 4.25: Final wind velocity map for the 1^st June of 2016 after the implementation of the KNN algorithm.

Along the time interval selected, looking carefully at all the distributions, one can find some events that make the measurements unreliable due to the limitations of the radar. Those events should be identified and excluded from the last analysis since they could affect significantly the final values computed statistically. In order to do so, distribution comparison techniques have been implemented. A standard distribution for each time step have been considered and then compared to each one in order to find these events. For example, one of the problems can be found on the 13^thof June, 2016. The map obtained from the application of this method for this day is shown in Figure 4.26b, whereas the original data are represented in Figure 4.26a.

Considering only the month of June as the launch window for Polar-Summer LDB missions, the data of each day in June for 2 years (2016 and 2017) have been statistically treated combining the wind maps. This way, mean values for every point in the map have been obtained as is shown in Figure 4.27a. In addition, the 95 percentile has also been computed. These values, shown in Figure 4.27b, will be used as the worst cold case during the ascent phase for this kind of balloon. The thermal control of instruments on board should be sized taking into account the

4. Planetary thermal environment for stratospheric balloon thermal design 79

(a) (b)

Figure 4.26: (a) Original wind velocity map of 13^th June 2016 and (b) map resulting after the treatment.

convective effect of the relative velocities of the system. As explained before, they can be derived from a dynamic model using wind data presented in this paper.

(a) (b)

Figure 4.27: (a) Mean values and (b) 95 percentile values of the month of June of years 2016 and 2017.