4.1 Principal Components and Loadings
4.1.2 NSY, 45
.9 kHz Transmitter
The signal path from NSY to Tihany is north–south oriented with a length of 1124 km. Due to the different orientation and higher frequency than GBZ, the annual variation of signal strength of NSY is considerably different. Typical profiles of the signal strength for each season appear in Figure 4.8.
The annual and diurnal variations of signal strength are presented in Figure 4.9. The sections of white represent bad or missing data. NSY appears to be more operationally stable than GBZ.
The diurnal variation of signal strength is clearly seen, with the nighttime signal being much stronger than the daytime signal. Once again, the sunrise and sunset times at 100 km altitude above the transmitter and receiver are indicated by the solid and dashed curves respectively. Un- like with the GBZ–Tihany path, these cross over at some point during the northern hemisphere spring and again in autumn. The passage of the dawn and dusk terminator produces pronounced dips in signal power. The dawn transition tends to consist of two distinct drops in power, with a separation of about two hours between them. The later power drop is not present throughout the year, seemingly absent during summer. The dusk terminator produces a singular power dip, which jumps between earlier and later times at approximately the same time of year as when the sunset times for the transmitter and receiver cross. These drops in power are due to mode conversion in the waveguide propagation as the sunrises or sets. Similarly to the GBZ–Tihany path, the dawn transition is more sharply defined than the dusk transition.
UT
Amplitude (dB)
0 4 8 12 16 20 24
−90−80−70−60−50−40
(a) Summer, 11 June 2009
UT
Amplitude (dB)
0 4 8 12 16 20 24
−65−60−55−50−45
(b) Autumn, 23 September 2008
UT
Amplitude (dB)
0 4 8 12 16 20 24
−80−70−60−50−40
(c) Winter, 20 December 2008
UT
Amplitude (dB)
0 4 8 12 16 20 24
−65−60−55−50−45
(d) Spring, 22 March 2009
Figure 4.8: Typical seasonal variation of amplitude of NSY. Note, the amplitude is measured in dB above an arbitrary reference level.
0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360
Day Number
0 4 8 12 16 20 24
UTC
0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360
Day Number
0 4 8 12 16 20 24
UTC
Receiver Transmitter
−80 −70 −60 −50 −40
dB
Figure 4.9: Annual signal strength variation for NSY, 45.9 kHz.
PC
% variance
0 5 10 15 20 25 30
01020304050
Figure 4.10: Variances accounted for by the principal components of NSY.
The variations of this signal are even more complex than that of GBZ, thus being an excellent candidate for PCA. The results from the PCA appear in Table 4.1.2. The first principal component accounts for 48.97% of the variance, less than the first principal component for GBZ. The second, third and fourth components account for 17.43%, 5.27% and 3.30% of the variance respectively.
Together, they account for 75% of the total variance in the data. Figure 4.10 shows the variance for each principal component. The first ten components seem to account for the major part of the variance in the data set.
Figure 4.11(a) shows the first principal component (PC 1), with the loadings in Figure 4.11(b).
This component expresses the general diurnal variation of the NSY signal strength. As seen from the component loadings, it is more indicative of the signal during the northern hemisphere winter, with the daylight hours being short and the two dips in signal power during sunrise. The difference in signal strength between day and night is also quite high.
Table 4.2: First 10 principal components of NSY.
PC Eigenvalue Variance (%) Summed Variance (%)
1 96.47 48.97 48.97
2 34.33 17.43 66.39
3 10.38 5.27 71.66
4 6.51 3.30 74.96
5 4.93 2.50 77.47
6 4.06 2.06 79.53
7 3.68 1.87 81.40
8 2.63 1.34 82.74
9 2.41 1.23 83.96
10 2.22 1.13 85.09
UT
dB
0 4 8 12 16 20 24
−15−10−50510
(a) PC 1
Month/Year
r
07/08 08/08 09/08 10/08 11/08 12/08 01/09 02/09 03/09 04/09 05/09
0.00.20.40.60.81.0
(b) Loadings of PC 1
Figure 4.11: First principal component signal and loadings for NSY.
UT
dB
0 4 8 12 16 20 24
−10−505
(a) PC 2
Month/Year
r
07/08 08/08 09/08 10/08 11/08 12/08 01/09 02/09 03/09 04/09 05/09
−0.6−0.4−0.20.00.20.40.60.8
(b) Loadings for PC 2
Figure 4.12: Second principal component signal and loadings for NSY.
UT
dB
0 4 8 12 16 20 24
−6−4−202468
(a) PC 3
Month/Year
r
07/08 08/08 09/08 10/08 11/08 12/08 01/09 02/09 03/09 04/09 05/09
−0.4−0.20.00.20.4
(b) Loadings of PC 3
Figure 4.13: Third principal component signal and loadings for NSY.
UT
dB
0 4 8 12 16 20 24
−10−505
(a) PC 4
Month/Year
r
07/08 08/08 09/08 10/08 11/08 12/08 01/09 02/09 03/09 04/09 05/09
−0.4−0.20.00.20.4
(b) Loadings of PC 4
Figure 4.14: Fourth principal component signal and loadings for NSY.
UT
dB
0 4 8 12 16 20 24
−6−4−2024
(a) PC 5
Month/Year
r
07/08 08/08 09/08 10/08 11/08 12/08 01/09 02/09 03/09 04/09 05/09
−0.4−0.20.00.20.4
(b) Loadings of PC 5
Figure 4.15: Fifth principal component signal and loadings for NSY.
Although all the original variables are positively correlated with PC 1, the correlations show a clear annual variation, with the difference between the summer and winter months quite large.
This is quite unlike the correlations of PC 1 for GBZ, which were all quite strongly correlated, with smaller variations between summer and winter.
The second principal component (PC 2) has an annual variation in the correlations with the original variables. Figure 4.12 shows that PC 2 is negatively correlated with the winter months, while having a positive correlation with the summer months. PC 2 has large drops in amplitude around 04:00 UT and 16:00 UT. The first drop extends until 07:00 UT, while the second is brief.
The addition of PC 2 to PC 1 for the summer months has the effect of increasing the signal strength of the daytime transmission, as well as broadening the length of the day. It also removes, to a certain extent, the first dip in the power during the dawn terminator passage. The winter months, being anticorrelated with PC 2, require the addition of the inverse of the signal. This results in a decrease in the daytime signal strength and a steepening of the dawn and dusk terminator passages. PC 2 also accentuates the initial dip in power during the dawn transition.
Figures 4.13 and 4.14 show the components and loadings for the third and fourth principal components. PC 3 has a semiannual variation in the loadings, with positive correlations around the equinoxes and negative correlations during solstices. This component affects the shape of the dawn and dusk terminator passages, either steepening or smoothing depending on the time of year. As is the case for the GBZ PCA results, analysis of further components becomes difficult.
PC 4 exhibits a triannual variation in its loadings, while PC 5’s loadings are randomly distributed.