The important TPMU goal is the validation and testing of the novel design of the instrument which is necessary for possible applications of TPMU design on future scientific missions. The similarities in time profiles of floating potential, electron temperatures and Kp index by adopting the method of cluster analysis using time was identified. The cluster time division is also similar and statistically significant This proves that the measurement of electron temperatures react physically and have only systematically biased. This method to analogous problems with measured data can be applied.

Fig.1: TPMU - PROBA II Microsatellite Instrument.

PROBA II satellite with the TPMU on board was launched on 2 November 2009. Orbit: Altitude between 700 and 800 km, Sun-synchronous, Inclination 98.298 degrees, Attitude control: Sun-pointing with automatic manoeuvring. Source: IAP ASCR, http://www.esa.int/Our_Activities/Technology/Proba_Missions/About_Proba-2

Electron Temperature and Floating Potential Measurement by TPMU - PROBA II Microsatellite Instrument as Dynamically Evolving System

Kateřina Podolská(1), František Hruška(2), and Vladimír Truhlík(3)

Institute of Atmospheric Physics ASCR, Prague, Czech Republic; (1) kapo@ufa.cas.cz, (2) fhr@ufa.cas.cz, (3) vtr@ufa.cas.cz

A dynamically evolving system is one that changes over time, often going through distinct steps or stages as it changes. One example of a dynamically evolving system is the seasonal variation and variations in solar activity. Cluster analysis was performed in the SAS 9.2TM software, use procedure FASTCLUS applied to time series. In detail is application of the procedure is described in (Corliss 2012). This computational technique is used to demonstrate how time intervals may be used to identify subgroups of electron temperature resp. floating potential in segmentation in cluster analysis. The object entering into the calculation is realization of a random vector with components Unixtime and Electron temperature resp. Floating potential described by the equation [1]:

X = (Unixtime, Electron temperature resp. Floating potential) [1]

The number of realizations of random vector in the reference period 05/2010 – 03/2013 is 1 780 134 (Te) and 222 518 (FP). During the calculation data was repeatedly distributed to 1-5 clusters in 10 iterations and the optimal number of clusters is selected. The homogeneity of the groups is measured by cluster mean square deviation. Centroid method for cluster identification was used [Sokal and Michener, 1958]. Cluster centroid is the median time variables, the the random vector component Unixtime in the cluster. Each random vector from the examined time series is within the computational processes classified into groups with similar characteristics. The distance between two clusters is defined by DKL= || xK - xL ||2. If d(x, y) = || xK – xL||2, then the combinatorial formula is:

DJM = (NKDJK + NLDJL ) / NM – (NK NL DKL) / NM2 [2]

where xi, ith observation (row vector if coordinate data), d(x, y) any distance or dissimilarity measure between observations or vectors x and y, DKL any distance or dissimilarity measure between clusters CK and CL,, NK number of observations in CK

Kth cluster, subset of (1, 2,…, n), xK mean vector for cluster CK. In the centroid method, the distance between two clusters is defined as the (squared) Euclidean distance between their centroids or means. The centroid method is more robust to outliers than most other hierarchical methods. The time distribution of belonging to groups then were compared with the timing phase of the solar cycle. The calculation was made separately for each series of the Electron temperature resp. Floating potential. Divided into clusters revealed that for Electron temperature resp. Floating potential are grouped into five clusters in terms of values of the Electron temperature resp. Floating potential. For a different number of clusters is not classification significant.

Thermal Plasma Measurement Unit (TPMU) scientific instrument was developed for PROBA II microsatellite and launched in November 2009. The device is working with limitations of scientific measurements caused very probably by installed onboard software. This brings lower data volume as it was planned. Affected are ion measurement and partially electron temperature measurement. This limited function of the instrument is stable and lasting since the beginning of the mission. The data are completed with orbital parameters. We use cluster analysis using time to study seasonal and geographical variations of the floating potential and the electron temperature. Analysis is performed separately for all seasons and Equatorial region, North and South hemisphere. The annual seasonal changes in the floating potential and electron temperature are reflected in the clusters identified in this analysis. Changes in the beginning, the end and duration of seasons over a period of years reflect also changes of Kp index. Using this stochastic cluster analysis method were able to utilize a higher volume of usable measured data and continue with the study of the scientific interesting effects and process the data statistically. Summer seasonal cooling or heating on the South or North hemisphere influence on the floating potential is in evidence.

METODOLOGY

•[Corliss, 2012] Corliss, D.J., Dynamically Evolving Systems: Cluster Analysis Using Time, SAS Global Forum, 2012, Paper 329-2012, pp. 2-3. •[Sokal and Michener, 1958] Sokal, R. R., and Michener, C. D., A statistical method for evaluating systematic relationships, Univ. Kansas Sci. BulL, 1958, 38, 1409-1438. [1.2.4,

1.2.5, 5.1, 5.4.1, 5.5.1]. • [Berghmans, 2013] Berghmans, D. et al, The PROBA2 Mission: The First Two Years of Solar Observation, Solar Physics, Volume 286, Issue 1, 2013.

REFERENCES

Fig.5: The boxplots of FP and Kp solar index in the period 06/2010–03/2013. The Te boxplots are divided by temperature above and below 4200 K. Plots are organized in groups by year-month. A box-and-whiskers plots display the mean, quartiles, and minimum and maximum observations for a data groups. TPMU measurement works in non-standard condition, only measurement of Te>4200K is possible.

Fig.4: Comparison of the floating potential TPMU data and Kp index. For the periods 06/07/2012–10/07/2012 and 13/07/2012–17/07/2012 were compared with the responding Kp index data at the time of geomagnetic storm.

Fig.3: Geographical visualisation of FP These plots visualise the floating potential FP data in geographical coordinates.Summer seasonal decrease of the floating potential plot is in evidence. Since 2013, the unit is turned on for a short period at the same time. The satellite is synchronized to the Sun, so measuring is in the same geographical coordinates, ie there is no global coverage. Geomagnetic equator and the 10th parallels north and south are drawn with red line.

CONCLUSIONS

• The satellite Proba2 telemetry data, the TPMU and the DSLP unit onboard measurement. • The geographical coordinates computed from Tle parametres by ORBL algorithm. • World Data Center for Geomagnetism, Kyoto University, Japan, [cit. 2013-04-15]. http:/wdc.kugi.kyoto-u.ac.jp/kp/index.html. • Space Physics Interactive Data Resource (SPIDR), National Geophysical Data Center, Boulder, USA, [cit. 2013-04-15]. http:/spidr.ngdc.noaa.gov/spidr/dataset.do?view=ionospheri.

DATA SOURCES

This study was supported in part by grant LH11123 of MSMT of the Czech Republic. We also thank to Thermal Plasma Measurement Unit Team ( Jiri Base, Jan Klas (+ 2010), Ivana Kolmasova) and J. Šmilauer for the ORBL software for computing geographical coordinates.

ACKNOWLEDGEMENTS

RESULTS OF THE CLUSTER ANALYSIS USING TIME

The time distribution of belonging to the clusters were compared with the timing of the Kp index changes. The optimal number of clusters for investigated time series was selected. Divide into clusters revealed that for electron temperature Te resp. floating potential FP and Kp index serie are grouped into five clusters in terms of values. For a different number of clusters is not classification significant. Results of the computed cluster analysis using time are in the Table 1. The homogeneity of the groups is measured by cluster mean square deviation Root-Mean-Square Standard Deviation (RMSSTD in Tab.1). In the first column of Tab.1 is Optimization criterion of computing, in the next colums are Cluter number, Frequency of cluster, Maximum distance from cluster seed (RADIUS), Distance to Nearest Cluster (GAP), Unixtime centroid value and centroid value of measured FP, Te and Kp index time serie. Vizualization of the computed cluster division of floating potential FP, Electron temperature Te TPMU data and Kp index is illustrated in the Figure 2. Belonging to the clusters and changing of time profiles are compared here. Year-month of changing of time profiles is marked in the picture. The change of time profile of FP and Kp index fits perfectly, for Te slightly less but still statistically significant.

Optimization

Criterion Cluster

Frequency

of Cluster RMSSTD RADIUS GAP UNIXTIME

Centroid

value

Floating potential FP

3662559.9 1 70869 4330142.6 11962479.5 19352348.8 1350447788 -0.6296

3662559.9 2 35849 2985413.6 7800158.6 16033196.3 1281397789 -0.5969

3662559.9 3 38304 3359961.3 9169497.5 15052396.8 1312483382 -0.6763

3662559.9 4 45900 3799405.9 9639119.7 18612057.9 1331095440 -0.3570

3662559.9 5 31596 2722499.1 7804522.9 15052396.8 1297430985 -0.2529

Electron temperature TE

3297732.9 1 3807 2688849.3 8674526.4 16138780.4 1310326657 6453.04

3297732.9 2 3654 1882925.6 7275805.7 15403946.4 1278783930 6479.32

3297732.9 3 6127 2609309.8 7655746.9 15403946.4 1294187877 6294.09

3297732.9 4 7217 3703294.9 12875210.5 17300982.0 1327627639 6313.06

3297732.9 5 9646 3941272.0 13096948.6 26087836.3 1353715476 6347.36

Kp index Kp

3662538.6 1 286792 2985322.8 7800323.7 16033038.3 1281397948 1.30

3662538.6 2 367190 3799304.2 9639276.4 18611912.9 1331095296 1.70

3662538.6 3 252768 2722461.4 7804476.2 15052396.8 1297430986 1.65

3662538.6 4 306432 3359922.9 9169558.3 15052396.8 1312483383 1.40

3662538.6 5 566952 4330115.8 11962486.5 19352493.8 1350447789 1.47

Fig.2: Vizualization of the computed cluster division of floating potential FP, electron temperature TPMU data and Kp index. In these figures is shown the color representation of belonging to the clusters for the period 2010/05–2013/03. Floating potential in left, electron temperature in the centre and Kp index in right. The clusters for all time series are marked by same color for similar time profiles.

Tab.1: Results of the cluster analysis using time computing. Table is divided into three parts for FP, Te and Kp index results.