3.2 Summary of Spread Parameters for the Nurmijärvi to Bruntingthorpe and Qaanaaq to Ny-Ålesund Paths
 Presented in Table 2 are the 95th percentile values of Doppler and delay spreads for two of the paths considered in this paper (NB and QN) for the period 14 March 2009 to 1 July 2012, a period spanning the current solar cycle minimum to around the recent peak (Figure 2).
Table 2. The 95th Percentiles of Doppler Spread and Delay Spread for the Period 14 March 2009 to 1 July 2012
|Doppler spread (Hz)|| || |
|Summer day||no data||1.0||1.0||1.5||1.5||1.5||1.5|
|Equinox day||QN||1.0||5.0||5.0||4.5||4.0||7.0||Not used|
|Summer day||no data||no data||3.5||3.5||3.5||7.0|
|Summer night||no data||1.5||2.5||2.0||2.0||3.0|
|Multipath (ms)|| |
|Summer day||no data||1.7||1.5||0.6||0.7||0.3||0.1|
|Equinox day||QN||0.7||0.9||0.5||0.3||0.2||0.3||Not used|
|Summer day||no data||no data||0.3||0.2||0.3||0.3|
|Summer night||no data||0.4||0.4||0.3||0.2||0.2|
 Doppler spreads observed on the trough path NB are small, all 95th percentiles being 2.0 Hz or less. This contrasts markedly with the polar cap path from QN where Doppler spread 95th percentile values range from 1.0 to 13.0 Hz, but are with few exceptions greater than the values for the trough path. The largest values tend to occur in winter. Interestingly, in summer, the spreads tend to be higher during the day, this being particularly marked at 14.36 MHz. In this case, the large daytime value of spread at the 95th percentile arises from observations from a relatively small number of days, over half of the samples where the Doppler spread is greater than 7 Hz come from just 2 days (mostly 29 May 2012, but a few samples from 13 May 2011). Multipath spreads tend to be smaller for the QN polar cap path than for the NB trough path.
3.3 Effects of Sunspot Number Variation
 In a previous paper [Stocker and Warrington, 2011], the behavior of the Doppler and delay spreads at sunspot maximum and sunspot minimum was found for paths along the trough. Since observations were only available at extreme sunspot values (less than 20 at sunspot minimum and more than 100 at sunspot maximum), it was not possible to predict what the spreads would be at intermediate values. Having continued to make measurements through the recent sunspot maximum, it is now possible to determine the behavior of the spreads over a range of moderate sunspot values. In order to do this, the spreads have been collected into bins of 13 month smoothed sunspot number (SSN) of values 0–10, 10–20, etc. for different propagation paths, seasons, and day and night. In order to extend the range of sunspot values available, measurements of the spreads from the UB path collected in 2001 have been used as an indication of those that would have been measured on the similar, but slightly longer, NB path. While the observations presented by Stocker and Warrington  indicate that this is a reasonable assumption for conditions of sunspot minimum, it is not certain that this will also be the case at sunspot maximum. However, propagation from similar ionospheric features (e.g., irregularities in the auroral oval) is likely to result in similar behavior in the spreads regardless of the path. The observations where the data are present in more than three bins appear to fall into five categories, the spread (1) is constant with SSN to the precision of the observations (~0.5 Hz in Doppler, 0.1 ms in CMPS), (2) increases suddenly at a particular value of SSN, (3) changes linearly with SSN, (4) peaks at a particular value of SSN, and (5) a trend cannot be identified, e.g., because there are large, but unsystematic variations in the spread.
 Examples of the first four types of behavior of spreads at the 95th percentile are given in Figure 4, where the spread values have been plotted at the middle of each SSN bin (i.e., 5, 15, etc.). For the first type, where a sudden increase occurs, the range over which the change occurs (e.g., in the top left panel, the highest SSN at the low level is 65, while the lowest SSN at the high level is 105) and the mean low and high levels (1.5 Hz and 4 Hz) can be defined. For the second type, the gradient and intercept of the least squares fit can be calculated (these are shown on the figure). Where there is a peak (category 4), the distribution can be partially characterized by the position of the peak (e.g., SSN = 35 in the bottom left panel) and the value at the peak (5 Hz in this case). The case presented in the third row, left column, has been characterized as a constant value of spread because the sudden increase at high sunspot numbers is within the precision of the measurements.
Figure 4. Examples of variation of spreads with smoothed sunspot number. (top row) A sudden increase in spread (left NB, 6.95 MHz, Winter night; right NB, 11.12 MHz, Equinox night) (second row) A linear change (left QN, 11.12 MHz, Equinox night; right NB, 11.12 MHz, Equinox day). (third row) Fixed value within the precision of the data (left NB, 6.95 MHz, Winter day; right QN, 11.12 MHz, Summer day). (bottom row) A peak in spread (left QN, 11.12 MHz, Equinox day; right NB, 14.36 MHz, Summer night). Note that points marked + are from UB and that only cases where there are more than 20 HF measurements are shown.
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 The behavior of the Doppler and composite multipath delay spreads is characterized for subauroral paths (i.e., NB and UB) in Tables 3 and 4, respectively, while that for polar cap path QN is given in Tables 5 and 6. In the tables, the “L” entries contain the constants to be used to construct a linear expression for the quantity. For example, in Table 4, the “L” numbers in the column under 11.12 MHz in “Equinox Day”, namely “0.019 + 0.6” correspond to the algebraic expression in the corresponding panel in Figure 4 (row 2, column 2): y = 0.019x + 0.6, in which y is the composite multipath spread and x is the SSN. The “P” entries show the SSN numbers at which a peak is located and the peak value. For example, in Table 4, the “P” numbers in the column under 14.36 MHz in “Summer Night”, namely 55–65, 0.4 correspond to the peaked distribution in the panel in Figure 4 (row 4, column 2). Tabulated “SI” values are to be read similarly for representation of the SSN dependence of the dependent variable characterized by a sudden increase at particular SSN values. “Fix” denotes a constant within the precision of the observations for all SSN.
Table 3. Behavior of 95th Percentile of Doppler Spread With Smoothed Sunspot Number for Nurmijärvi-Bruntingthorpe (Also Including Uppsala-Bruntingthorpe Data for 2001)a
|Day||ND||Fix = 1.5||Fix = 1.5||SI:65–105, 1.5–2.5||SI:65–105, 1.5–2.2|
|Night||Fix = 1.5||SI:65–105, 1.5–4||ND||SI:65–105, 1.7–11.1||SI:35–65, 1.3–7.4|
|Day||ND||SI:65–105, 1.0–1.9||Fix = 1.0||Fix = 1.5||Fix = 1.5|
|Night||L:0.009 + 0.9||SI:65–105, 1.5–2.9||Fix = 1.0||SI:65–105, 1.5–7.3||SI:65–105, 1.4–6.4|
|Day||ND||ND||ND||Fix = 1.5||Fix = 1.5|
|Night||Fix = 1.0||Fix = 1.5||Fix = 1.0||Fix = 1.5||Fix = 1.5|
Table 4. Behavior of 95th Percentile of Composite Multipath Spread With Smoothed Sunspot Number for Nurmijärvi-Bruntingthorpe (Also Including Uppsala-Bruntingthorpe Data for 2001)a
|Day||ND||ND||L:0.025 + 1.0||L:0.019 + 0.3||SI:35–65, 0.2–1.2|
|Night||L:0.007 + 1.1||SI:65–105, 0.3–2.5||ND||SI:105–115, 0.4–3.7||SI:65–105, 0.2–1.5|
|Day||ND||ND||L:0.009 + 1.6||L:0.019 + 0.6||L:0.011 + 0.1|
|Night||L:0.007 + 2.4||L:0.014 + 0.6||L:0.018 + 0.2||L:0.005 + 0.2||L:0.002 + 0.1|
|Day||ND||ND||ND||L:0.011 + 0.5||ND|
|Night||L:-0.011 + 4.5||L:0.013 + 1.5||L:0.022 + 0.8||L:0.003 + 0.4||P:55–65, 0.4|
Table 5. Behavior of 95th Percentile of Doppler Spread With Smoothed Sunspot Number for Qaanaaq to Ny-Ålesunda
|Day||L:0.044 + 4.3||L:0.023 + 4.5||ND||L:−0.039 + 5.5||ND|
|Night||SI:5−25, 3.5–6.3||SI:5–25, 3.0–6.5||ND||ND||ND|
|Day||L:0.041 + 3.2||L:0.030 + 3.6||SI:5–15, 3.5–5.0||P:35, 5.0||ND|
|Night||ND||SI:5–15, 2.5–5.9||SI:5–15, 2.0–5.7||L:−0.080 + 7.1||L:0.128 + 2.5|
|Day||ND||ND||L:0.034 + 2.5||L:−0.026 + 3.3||ND|
|Night||ND||L:0.022 + 1.7||SI:55–65, 2.3–4.5||L:−0.041 + 3.5||ND|
Table 6. Behavior of 95th Percentile of Composite Multipath Spread With Smoothed Sunspot Number for Qanaaq-Ny-Ålesunda
|Day||L:0.015 + 0.4||L:0.005 + 0.3||ND||Fix = 0.2||ND|
|Night||L:0.007 + 0.1||ND||ND||ND||ND|
|Day||ND||L:0.005 + 0.3||Fix = 0.3||Fix = 0.2||L:0.003 + 0.2|
|Night||ND||L:0.003 + 0.3||L:0.004 + 0.1||Fix = 0.2||Fix = 0.2|
|Day||ND||ND||Fix = 0.2||Fix = 0.2||ND|
|Night||ND||L:0.005 + 0.3||Fix = 0.2||Fix = 0.1||ND|
 Although observations are available at 10.39 MHz and 18.38 MHz for NB, a change in transmission schedule part of the way through the period reported here means that there is insufficient range in sunspot values to draw sensible conclusions and these are omitted from Tables 3 and 4. Furthermore, only data from NB are available at 8.01 MHz (since this frequency was not used for UL in 2001), so the SSN range is limited to 0–70 at this frequency. The range of SSN is similarly limited for the QN observations in Tables 5 and 6. In addition, there are insufficient observations at 4.64 MHz on the QN path and therefore this frequency has been omitted.
 The Doppler spread on the subauroral paths (NB and UB) does not change with sunspot number during the day at the lower frequencies (4.64 to 8.01 MHz), while there is a small sudden increase between SSN = 65 and SSN = 105 at the higher frequencies. The absence of data at SSN between these values means that it is not possible to determine how the spread changes in this range (e.g., whether there is a gradual change from one state to the other or a sudden change)—this limitation of the current data set applies to all of the following discussion. At night, the step in Doppler spread is larger (e.g., at 11.12 MHz winter night, the Doppler spread is 1.7 Hz for SSN ≤ 65 and 11.1 Hz for SSN ≥ 105) and is observed on all frequencies except 4.64 MHz and 8.01 MHz (although note that there are no observations at SSN > 65 for 8.01 MHz). The composite multipath spread tends to increase linearly with SSN, although there are a few examples (e.g., 11.12 MHz, winter night) where there is a sudden increase at high SSN. The behavior of the spreads is consistent with the signal scattering from irregularities in the poleward wall of the trough or in the auroral oval previously discussed [Warrington and Stocker, 2003; Stocker and Warrington, 2011; Siddle et al., 2004a, 2004b; Stocker et al., 2009]. Such scattering will lead to higher Doppler spread since the irregularities will be moving at different velocities, and generally higher multipath spread since the time-of-flight of such off-great circle propagation modes is much longer than that of the on-great-circle modes that might also be present [e.g., see Siddle et al., 2004a, 2004b]. At solar minimum, propagation via the auroral oval or poleward wall of the trough was significantly less common than at solar maximum [Warrington et al., 2007] and hence the Doppler and delay spreads are also lower at lower levels of solar activity.
 On the polar cap path (QN), at frequencies up to 10.39 MHz, the Doppler spread tends to increase with SSN, either linearly or with a sudden increase at relatively low SSN (e.g., for 6.95 MHz winter night, the Doppler spread is 3.5 Hz at SSN = 5 and 6.3 Hz at SSN ≥ 25). The behavior is very different at 11.12 MHz, where the Doppler spread either peaks at SSN = 35 or more usually decreases with increasing SSN. The trends are unclear at 14.36 MHz, except in one case (Equinox night) where it increases with increasing SSN. It is also noteworthy that the Doppler spreads are generally higher than those observed on the subauroral paths except when the latter are affected by scatter, e.g., during winter night. Although at a much higher radio frequency, it is interesting to note that polar patches are a significant cause of VHF/UHF scintillations and patch activity, and hence scintillation increases, with SSN and during the winter [Dandekar, 2002; Basu et al., 1988]. In general, an increase in Doppler spread is apparent with increasing SSN. However, this is inconsistent with the decrease in Doppler spread with SSN for 11.12 MHz. For example, for SSN = 60–70, the median and 95th percentile values of the Doppler spread are 1.0 and 1.5 Hz for 11.12 MHz, while they are 1.5 Hz and 5.5 Hz for 10.39 MHz. On days where high spreads are seen at 10.39 MHz, the propagation modes at the two frequencies appear to be the same (so propagation via a 1E mode is not leading to a reduced spread at 11.12 MHz). However, the signal strength at 11.12 MHz is generally lower than that observed at 10.39 MHz, so it is possible that when the signal is highly Doppler spread the level of the individual signal components is reduced to below the noise floor and hence the spread signals are not detected. The composite multipath spread for the lower frequencies increases with SSN, while for the higher frequencies is generally constant. For the lower frequencies, the increase in SSN will tend to increase the number of propagation modes available and hence the multipath spread, but for the higher frequencies, propagation is generally via a single hop irrespective of SSN.