HF radio propagation was observed regularly during the night at frequencies above the classical Maximum Usable Frequency (MUF) on the circuit from Fort Collins, Colorado, to Boston, Massachusetts, during 2003 (McNamara et al., 2006). This propagation was attributed to above-the-MUF propagation, in the sense of normal refraction by over-dense regions in the F2 layer of the ionosphere, following Wheeler (1966). Similar propagation was also observed on a regular basis on the Ottawa to Boston circuit, at an operating frequency of 7.335 MHz. We have reanalyzed the nighttime Ottawa to Boston propagation in conjunction with observations of foF2 recorded by the digisonde at Millstone Hill (near Boston). Normal propagation (via refraction) would be supported on this circuit only when foF2 exceeds the equivalent vertical frequency, which is ∼5.7 MHz. The actual propagation extends through the midnight to dawn period even when foF2 drops below 4 MHz, with signal powers decreasing from about −80 dBW to −110 dBW. We deduce that there are three possible modes of propagation that are, in order of appearance: (1) normal refraction when foF2 exceeds 5.7 MHz; (2) “sporadic” reflection from large scale irregularities (tens of kilometers) with plasma frequencies that exceed 5.7 MHz in a lower density background; and (3) a 2-hop ground side scatter mode with hop lengths greater than the 7.335 MHz skip distance. The second mechanism is the one discussed by Wheeler (1966).
 The observations discussed here are part of a larger set that was collected on multiple circuits and frequencies during 2003 [McNamara et al., 2006] (hereinafter Paper A). The observed transmissions were from the time standard stations at Fort Collins, Colorado (WWV) and Ottawa, Canada (CHU). The receiving site was at Hanscom Air Force Base (HAFB), near Boston. The circuit lengths were 2820 km (WWV-HAFB) and 476 km (CHU-HAFB). The monthly median observed powers (in dBW, dB above a watt) are shown as a function of universal time in several figures in Paper A (9: CHU 3.330 MHz; 10: CHU 7.335 MHz; 11: WWV 5.0 MHz; 12: WWV 10 MHz). We are concerned here mainly with the CHU propagation on 3.330, 7.335 and 14.670 MHz, because some of the propagation is clearly not via normal refraction, and we have ionograms from a nearby ionosonde at Millstone Hill to constrain our interpretations.
 The predicted monthly median maximum usable frequencies (MUF) given by VOACAP [Lane, 2001] are given in Figure 2 (CHU) and Figure 3 (WWV) of paper A. Figure 12 of Paper A shows that the observed WWV 10 MHz powers drop below −100 dBW in several months at 08–10 UT (∼02–04 LT at the circuit midpoint). The failure of the observed powers to follow a smooth diurnal curve (Figure 13 of Paper A) was attributed to absence of the normal propagation mechanism, which is refraction. The existence of weaker signals was attributed to above-the-MUF propagation as discussed by Wheeler , and included in VOACAP.
 Above-the-MUF propagation was investigated by M. L. Phillips and W. Abel in the mid-to-late 1950s. Their report seems to be no longer available, but their work was summarized by Wheeler . The Phillips-Abel theory attributes above-the-MUF propagation to refraction by “quasi-random elemental patches of ionization” that have a higher electron density than the background plasma. These patches support propagation by normal refraction at higher frequencies than does the background plasma. Thus if the predicted MUF is correct, propagation will occur at frequencies above the MUF. The power of signals at frequencies above the MUF will depend on the nature and number of the patches. The larger the “equivalent reflecting area” of the patches that have sufficient densities, the higher the signal power. The received signal power would be lower than for the normal F-layer propagation mode. Wheeler found that the path losses predicted by Phillips and Abel agreed well with observations between Maryland and Southern California. These authors related the observed powers to the values of foF2 given by several ionosondes along their very long circuits. For the 2003 CHU-HAFB observations, we have access to ionograms from an ionosonde at Millstone Hill (42.6°N, 288.5°E), which is very close to HAFB (42.5°N, 288.7°E). Since the CHU-HAFB circuit length is 476 km, this ionosonde is less than 240 km from the circuit midpoint, and close enough to expect very high correlations between ionosonde and midpoint values of foF2.
 We have manually rescaled the hourly Digisonde ionograms from Millstone Hill using ARTIST 5 [Galkin et al., 2008] for September and October 2003. Millstone Hill has a large number of prohibited frequency bands that the ionosonde must skip, making it a real challenge for ionogram autoscaling systems such as ARTIST [Reinisch et al., 2005]. A separate table was made during the rescaling to indicate if the F2 ionogram traces were resolved (the O and X traces are clearly separate traces) or unresolved (spread F echoes cover the whole foF2 to fxF2 frequency range). This distinction was drawn in case the low-power nighttime echoes were simply due to scatter by the irregularities that appear on the ionograms as frequency spreading around the foF2 and fxF2 asymptotes (which they appear not to be). The two months had some very disturbed periods, with Ap reaching 80, and there was evidence of the midlatitude trough on some days. The signal powers for the disturbed days have been excluded in one of two ways: (1) foF2 could not be scaled (manually) because of the presence of spread F on disturbed days; and/or (2) the signals went below the required SNR of 3 dB. Thus the data being considered here were for only quiet or relatively quiet days.
Section 2 of the paper describes the geometry of the CHU-HAFB circuit. The most important feature of this propagation is the difference between a layer critical frequency and the equivalent vertical frequency for each of the three operating frequencies. A normal refraction mode will be supported if the equivalent vertical frequency is less than the corresponding layer critical frequency. Section 3 presents some typical signal power observations for 7.335 MHz signals on individual days. This is the most interesting CHU frequency, because 3.330 MHz is almost always supported (albeit severely attenuated during the day), while 14.670 MHz is observed only at night, and then at signal-to-noise ratios (SNR) typically less than 5 dB. Observations are considered unreliable and therefore discarded if the SNR is less than 3 dB. Section 4 presents a mass plot of the 7.335 MHz signal power for September 2003, which illustrates the main features of the propagation. The nighttime propagation seems to have no correlation with spread F echoes on the Millstone Hill ionograms, as shown in section 5. Section 6 compares the monthly median values of foF2 and signal power, and shows how they decrease together after sunset. Section 7 compares sample CHU observations at three frequencies, qualitatively illustrating the approximate (f)−4 variation of signal power. Section 8 presents sample WWV-HAFB observations on the three WWV frequencies. Section 9 compares the observed powers with those predicted for a ground side scatter propagation mode. Section 10 summarises the observations and conclusions in terms of three possible nighttime propagation modes.
2. Circuit Geometry
 The CHU-HAFB circuit is 476 km in length. For normal F-layer reflection heights, the takeoff angle δ would be ∼51° (depending on the actual reflection height). For this short circuit, the equivalent vertical frequency fv would be approximately sin δ times the operating frequency [Davies, 1990, section 6.3]. For 7.335 MHz, fv = 5.7 MHz. In other words, if foF2 exceeds 5.7 MHz, a normal 1F refraction mode would be supported. For E or Es reflection at 110 km with a takeoff angle of ∼24°, fv = 3.0 MHz. The transmitting antennas are vertical dipoles with a wide vertical pattern, so both the E and F modes would be excited. The equivalent vertical frequencies for the three operating frequencies and two reflecting layers are given in Table 1.
Table 1. Equivalent Vertical Frequencies for the Three Operating Frequencies and Two Reflecting Layers
Takeoff Angle (deg)
 F-layer propagation would be supported on 3.330 MHz for virtually all days and hours during the observing period (January–October 2003), since foF2 usually exceeds 2.6 MHz. Normal F-layer propagation at 7.335 MHz would not be supported all through the night, since foF2 regularly falls below 5.7 MHz. F-layer propagation at 14.670 MHz would not usually be supported during 2003, because foF2 only rarely reaches 11.4 MHz. Propagation could occur at 3.330 MHz via the normal E layer when foE exceeds 1.4 MHz, which is for most of the day. However, the received powers for this frequency would be very low during the day because of D-region absorption. The 7.335 MHz signals could propagate via the normal E layer when foE exceeds 3.0 MHz, during the middle of the day.
3. Representative CHU Observations for Individual Days
Figure 1 shows the 7.335 MHz observations for day 244 (1 September) versus universal time. The observations at each frequency were made every 5 min.
 The daytime propagation (11 to 23 UT) shows the powers reaching their lowest values at ∼17 UT or noon, in step with HF absorption, which maximizes at noon. The daytime observations also show deep fades of ∼10 dB superimposed on the background ±5 dB fades. These are presumably the result of polarization fading between the ordinary and extraordinary mode signals. Note that the 5-min sampling interval is too coarse to catch all of the polarization fades, or to characterize any faster fades.
 We are concerned mainly with the propagation from about 02 to 10 UT (21 to 05 LT). The day 244 and other sets of observations show very little evidence of deep fading at night, which supports an interpretation of the propagation in terms of scattering rather than normal refraction. The 01–09 UT ionograms for day 244 exhibited spread F, but there is no obvious qualitative difference between the received signals for this night and other nights for which spread F was not observed. The postdawn increase in the power occurs as foF2 increases from 5.4 MHz at 1100 UT to 6.2 MHz at 1115 UT. Recall that foF2 must exceed 5.7 MHz for normal propagation to occur.
 The spikes in power that rise above −70 dBW, such as at 06 UT in Figure 1, are probably the result of reflection by sporadic E (Es) layers at the circuit midpoint, although there is no one-to-one correspondence between their occurrence and the occurrence of Es on the ionograms. This lack of correspondence is not surprising, because the correlation distance for Es layers is ∼100 km, and the ionosonde is ∼240 km from the circuit midpoint. The blanketing frequency for the Es layer would need to be ∼3.0 MHz for the layer to reflect 7.335 MHz signals. The levels reached by these spikes tend to be higher for longer durations, suggesting that the Es clouds then have larger horizontal sizes.
Figure 2 shows the 3.330 MHz powers for the same day (244) as for Figure 1. The main feature of the 3.330 MHz propagation is the low signal levels during the day, which result from high levels of HF absorption. In fact, the observed SNR was often below the required minimum to ensure that the measurements are reliable (set to 3 dB). The nighttime propagation would be via normal refraction, which leads to deep polarization fades. The 14.670 MHz signals were detected on this day only between 00 and 04 UT, with powers of −116 ± 4 dBW.
4. The 7.335 MHz Observations for All Days in September
 Different ways of presenting the observations highlight different aspects of the propagation. Figure 3 shows a simple mass plot of all September 5-min signal power observations on 7.335 MHz.
 Starting at 00 UT (19 LT), the upper envelope of the power decreases throughout the night, and this set of data points extends through until ∼15 UT. The scattered points with high powers correspond to bursts of Es propagation (as for day 244, Figure 1). The monthly median value of foF2 increases through the equivalent vertical frequency (5.7 MHz) at 12 UT, which is when the signals with powers up to −70 dBW begin to be supported again. (The median values of foF2 are included as part of the later Figure 6.) The data points at −105 dBW after 12 UT correspond to those days for which the value of foF2 lay well below the median, such as day 253. The rate at which the propagation switches to the normal 1F mode after dawn on a given day depends on the steepness of the rise of foF2 on that day. For example, day 284 showed a very steep rise as foF2 increased from 5.5 MHz at 1145 UT to 5.9 MHz at 1200 UT. The minimum in the upper envelope of the distribution at 17 to 18 UT (12 to 13 LT) is set by the HF absorption, which would be a maximum at that time of day. Unfortunately, it is not possible to separate daily changes in the attenuation of the transmitted signal due to absorption from those due to changes in the height of the reflecting layer that change the free-space loss.
 The July version of Figure 3 shows very little “white space” (pixels with no echoes) for the higher powers at night, presumably because of the increased presence of sporadic E propagation. Midlatitude Es is basically a summer phenomenon. When these data points are ignored, the remaining points look very much like those for September (Figure 3). Figure 10 of Paper A shows that the median powers at ∼08 UT are ∼5 dB higher for July (upper set of red disks) than for September. (The lower set of red disks in the figure corresponds to the October data.) The median July powers given in Figure 10 of Paper A are thus erroneous, since they represent a mixture of an Es propagation mode and an above-the-MUF propagation mode. Improper mode identification is one of the problems that arise when comparing predicted and observed HF signal powers without observations of the azimuth and elevation of the incoming signals.
5. Effects of Spread Ionogram F2 Traces
 The nighttime Millstone Hill ionograms often showed spread F2 traces, which are an indication of irregularities in the F2 region. Those ionograms with extremely spread traces that prevented the scaling of foF2 have been ignored. The ionograms for which foF2 could be scaled were grouped into two categories: high spread-F and low spread-F. When the frequency spread increased to the point that the entire region of the ionogram between the foF2 and fxF2 vertical asymptotes was filled with echoes, an ionogram was said to have high spread; otherwise the spread was categorized as low. Figure 4 shows the signal strength data from high spread-F times, which are usually at night.
Figure 5 shows the data for those ionograms in which the vertical asymptotes for foF2 and fxF2 were well separated (i.e., resolved, low spread F). The point of interest with these two figures is that during the night (00–12 UT, 19–07 LT) the received signal strength on 7.335 MHz is virtually the same for both high and low spread-F conditions. Thus the above-the-MUF propagation does not seem to be related to the irregularities that cause spread-F.
6. Monthly Median Values of foF2 and Signal Power
Figure 6 shows the monthly median values of foF2 at Millstone Hill and the median signal powers on 7.335 MHz for September 2003. The values of foF2 have been normalized to the equivalent vertical frequency of 5.7 MHz, and the powers have been rescaled to fit the data points on the same vertical scale as foF2.
 The purpose of this plot is to show that the observed powers decrease throughout the night in step with foF2. The results are similar for the October data. This figure excludes those ionograms that showed extreme spread F, since the values of foF2 were then uncertain and not scaled.
 There is not a good one-to-one correspondence between the hourly values of signal power and foF2. Basically, there are two sets of data, depending on whether foF2 is greater or less than 5.7 MHz. The median values of foF2 lie below 5.7 MHz from 00 to 12 UT, i.e., 19 to 07 LT. The powers are ∼15 dBW lower when foF2 is below 5.7 MHz. There is also not a good one-to-one correspondence between the signal power and the height of mirror reflection (the ionogram virtual height at 5.7 MHz), even at night when HF absorption is very small.
7. Comparisons of CHU Observations at Three Frequencies
 If the nighttime propagation is supported by an ionospheric scattering mechanism, it would be expected that the signal power would fall off with increasing wave frequency. As is well known, the amplitude of a signal scattered by the ionosphere depends on the perturbations Δɛ to the permittivity ɛ. Ignoring the magnetic field, Δɛ depends on the operating frequency as (f)−2 [Davies, 1990, equation (3.11)]. The power in the scattered signal depends on the square of the amplitude, and thus on (f)−4. We could therefore expect the observed powers to drop off as (f)−4. We have made multiple plots that show the received nighttime powers for each operating frequency. Figure 7 shows the received powers for day 264 (21 September). Note that the 7.335 MHz powers have been decreased by 5.2 dBW (10 kW to 3 kW), to normalize the three transmitter powers to 3 kW.
 Day 264 was selected because the 3.330 MHz powers dropped down to −95 dBW at different times, presumably when the normal 1F refraction mode failed because foF2 went below the required ∼2.6 MHz, revealing the ever-present scatter mode(s). In fact, the dropouts on some nights are suggestive of polarization fading, but the same floor of −95 dBW is reached on other nights that do not show deep fades. The ionograms for day 264 showed spread traces from 02 to 10 UT, making it impossible to obtain reliable values of foF2. However, the values definitely went below 3 MHz between 07 and 10 UT. The high powers between ∼0630 to 0700 UT were probably due to Es propagation. The ionograms showed Es traces out to 4.7 MHz during this interval, confirming this interpretation. The 7.335 MHz signals have a floor at about −110 dBW, and the 14.670 MHz signals have a floor at about −125 dBW. These approximate levels, −95, −110 and −125 dBW hold for all of the nights considered. For a frequency dependence of (f)−4, the differences between the powers would be 13.7 and 12.0 dBW, versus the observed differences of 15 dBW. Given the uncertainties associated with determining the observed power levels, these levels are consistent with an ionospheric scattering interpretation when foF2 falls below 5.7 MHz.
8. Observations of WWV Signals
 We return now to the WWV May 2003 observations on 10 MHz which were discussed in Paper A (Figures 12 and 13). Figures 8 and 9show the observed signal powers for days 121 (1 May) and 137 (17 May), for the three WWV frequencies.
 At 08 UT (∼02 LT at the circuit midpoint), the 10 MHz power is about −115 dBW on day 121, and about −90 dBW on day 137 (ignoring the deep fade). There are clear morphological differences between the signal variations for the two days, indicating two different propagation modes. We propose that the day 137 propagation is via a normal 1F refraction mode, while the day 121 propagation with its weaker signals is via a scatter mode, as seen on the CHU-HAFB circuit. The 15 and 20 MHz signals drop out sooner than the 10 MHz signals, as expected. Note that these higher frequency signals often decreased to levels near the noise level. Data points are not plotted if the SNR is less than 3 dB. We do not attempt any further interpretations because the nearest ionosonde was over 1000 km from the circuit midpoint.
9. Ground Side-Scatter Loss
Gibson and Bradley  attribute above-the-MUF propagation to a 2-hop ground side-scatter mode [see, e.g., Davies, 1990, Figure 6.29], rather than to ionospheric scattering. In the ground side-scatter mode, the transmitted signals are scattered from the ground at a range exceeding the skip distance, and thence to the receiver. The ITU Recommendation ITU-R P.533-8 [ITU, 2005] is based on the same propagation mode. For frequencies f > fb (the basic MUF), the ITU formula for the above-the-MUF loss is:
or 62 dB, whichever is the smaller.
Figure 10 shows the corresponding values of Lm and the observed power for each hour of September 2003 between 00 and 09 UT (that had scalable values of foF2). The value of fb for each hour was derived from the scaled values of foF2 and M(3000)F2, the obliquity factor for the actual circuit length being derived from M(3000)F2.
 The straight line is the least squares fit line, drawn through the extra plotting points at −80 and −110 dbW. The 201 data points include the values of foF2 that were associated with spread F (both resolved and unresolved). The observed median power at 00 UT for this month is −81 dbW (Figure 10 of Paper A), so the line should pass actually through the point (−81, 0). The correlation coefficient for this set of data is −0.74, supporting the ITU model. The correlation coefficient for equation (1) of Gibson and Bradley  is −0.69. For the October 2003 data, the ITU correlation coefficient was −0.56. October was a very disturbed month, and the data count was only 128. Lower correlation coefficients were found for September when the ASAPS  values of the monthly median MUF were used in place of the individual values derived from the Millstone Hill ionograms.
 The observed (f)−4 frequency dependence of the received power described in sections 7 and 8 is also consistent with ground side scatter. As the operating frequency increases, so does the skip distance. The Poynting flux decreases with distance R as 1/R2. Thus, two-hop propagation results in a ∼1/R12 · 1/R22 decrease, provided the ground scattering efficiency does not depend on the wave frequency. Since both R1 and R2 are roughly proportional to the operating frequency, the observed frequency dependence of the power should be approximately (f)−4.
 While the observed (f)−4 frequency dependence indicates a scattering mechanism, it is not possible to distinguish between scattering by the ground and scattering by ionospheric irregularities, since both have the same frequency dependence. However, the weight of other experiments (such as described by Gibson and Bradley [1991, and references therein]) moves us to accept ground side scatter as the scattering mechanism. We noted in section 5 that the observed above-the-MUF propagation does not seem to be related to the ionospheric irregularities that cause spread-F, while in section 5 we commented that the received powers were not correlated with the height of mirror reflection. These are more reasons for accepting the ground-based interpretation. It seems likely that the ground side scatter interpretation can also be applied to the WWV-HAFB observations, for which we had no ionosonde data close to the reflection point.
 We deduce that the nighttime propagation of 7.335 MHz signals starts off as normal refraction until foF2 falls through 5.7 MHz. This is possibly followed by an interval of indefinite length during which the signals are reflected from over-dense irregularities. As the night continues, the density of these irregularities falls below 5.7 MHz, and the propagation is supported by a ground side scatter mode. There would also be an interval of X-mode-only propagation, when foF2 drops below the equivalent vertical frequency while this latter frequency is still below fxF2. There would be no polarization fading in this interval. We have, in fact, seen no clear-cut examples of this effect, but did not automate the search.