Potential worst-case selection

Once the albedo and OLR values have been obtained, it is necessary to filter the data distribution in Figure 4.5 to avoid sporadic points located in very low density areas. This means the elimination of points isolated from the majority (outliers), because they would provide a very unlikely environment with values that deviate greatly from their nearest points. In order to carry out this task, a grid-density based clustering algorithm [64] has been chosen as the most appropriate method due to the amount of data to be managed.

4. Planetary thermal environment for stratospheric balloon thermal design 55

Figure 4.5: Distribution of albedo and OLR for the considered region and period of time.

Figure 4.6: Six hours average TSI data measured by SORCE mission from June 26^th 2015 to June 26^th 2018

For this algorithm implementation, a grid of 100 x 100 cells on the distribution has been chosen. The grid density is defined by the number of the data points mapped on the grid. If a density threshold is established, it is possible to classify grids into sporadic or dense depending on whether its density is higher than that threshold value or not. Establishing ann-grid and rejecting points in sporadic grids, a new distribution of albedo-OLR without sporadic points values is obtained. For this algorithm implementation, a density threshold of 10 points in each cell has been established. This data treatment has supposed a data reduction of 0.03 %, which is negligible when compared to the total amount of pairs. As can be seen in Figure 4.7, the isolated points have mostly disappeared.

Once the new distribution is obtained, the study focuses on the identification of the data pairs leading to hot and cold worst-cases. An envelope of potential hot

Figure 4.7: Albedo and OLR distributions after grid-density clustering.

cases and an envelope of potential cold cases for a given confidence level are defined for this purpose within the whole cloud of pairs. This reduces considerably the amount of data managed, allowing a parametric sweep study to be performed.

In a similar way as is done in [17], where the tails of the individual distributions of albedo and OLR are cut with a certain level of confidence, in this work, the 2-D cloud of points (a, OLR) is cut with an envelope line to get rid of the pairs with very low probability or, better said, a very short potential time of exposure to these conditions. That is, the selection of possible worst hot cases has been based on obtaining in the cloud of points (a, OLR) an iso-probability line, or combination of albedo and OLR values which would produce the maximum temperatures on the payload for the level of confidence required. To identify the points of this line, it has been necessary to quantify the amount of points with higher albedo and OLR than the pair evaluated. Similarly, for the selection of possible worst cold cases, the amount of points with lower albedo and OLR than the combination evaluated has been taken into account.

A probability of 99.98 % has been used for this purpose. Defining that probability as the percentage of points which fulfil the established criteria, it is possible to obtain possible worst cases along the 2-D distribution. The results are displayed in Figure 4.8. There, the hot and cold points representing this probability limit are plotted within the cloud (a, OLR). Furthermore, once these points are obtained, to ease its further implementation in the thermal model, two regression curves have been calculated, one for possible worst cold cases and another for possible worst hot cases. These two curves are also shown in Figure 4.8 and, as will be explained in the following sections, they will be used for a parametric study of the influence

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Figure 4.8: Potential worst hot and cold case points and regression curves.

thermo-optical properties. As can be observed, in these lines the correlation between a and OLR is inverse, if one increases, the other decreases.

4.2.2.1 SZA influence

As it is explained in [15], albedo and OLR are partially correlated. In order to select a possible pair of values, both should be treated as a 2D data distribution.

However, if a higher level of accuracy is required, another parameter should be taken into account. Data used to obtain these curves also depend on the Solar Zenith Angle. The higher the SZA, the higher the albedo. This phenomenon occurs due to the angular models used in the estimation of the earth’s radiation budget at the TOA from satellite-measured radiances. The correlation of used data with Solar Zenith Angle is shown in Figure 4.9.

Figure 4.9: Correlation of albedo and OLR data with Solar Zenith Angle.

Potential worst cases have been defined for several Solar Zenith Angle. Curves corresponding with the potential worst hot and cold cases have been obtained using

the same criteria as in [15]. They represent points with an equal probability of finding points with a higher albedo and OLR for the hot case and vice versa for the cold case.

These points cause a higher or lower temperature on the system for the hot and cold case respectively. The 2D distributions for the lowest and highest SZA in the region and epoch of study are shown in Figure 4.10a and Figure 4.10b respectively.

(a) (b)

Figure 4.10: Albedo to OLR correlation for a SZA of (a) 45.5° and (b) 87.7°.