Observations of HF signal powers on two circuits in North America have been compared with the values predicted by two HF propagation programs, Voice of America Coverage Analysis Program (VOACAP) and Advanced Stand Alone Prediction System (ASAPS). Neither program consistently provided the more reliable predicted signal powers. For the longer circuit considered (2820 km WWV Fort Collins to Hanscom Air Force Base), ASAPS was found to be the more accurate program for the lower frequencies (at night), while VOACAP was the more accurate for the higher frequencies (during the day). The RMS errors ranged from a few decibels to 15 dB. For daytime 7.335 MHz propagation on the 490 km CHU Ottawa to Hanscom Air Force Base circuit, the VOACAP RMS errors (∼4 dB) were less than the ASAPS RMS errors (∼8 dB). The errors for the two programs were very similar for 3.330 MHz propagation, peaking at ∼9 dB just after sunrise and just before sunset and ∼3 dB during the night.
 This paper describes observations of the power of radio signals received from multifrequency time standard HF transmitters on two midlatitude circuits in North America. The observations were collected primarily for use as ground truth data for validation of HF signal powers predicted by the USAF Operational Space Environment Network Display (OpSEND) suite of applications running at the Air Force Weather Agency [Bishop et al., 2004]. The OpSEND HF illumination maps and real-time HF communication performance calculations determine signal powers and area coverage by numerical techniques that include ray tracing through a data assimilation model of the ionosphere.
 Observations of signal power were made using a standard calibrated HF receiver, preamp and antenna, monitoring time standard signals from WWV, Fort Collins, Colorado, on 2.5, 5, 10, 15 and 20 MHz, and from CHU, Ottawa, on 3.330, 7.335 and 14.670 MHz. The transmitting antennas at both Fort Collins and Ottawa are oriented vertically, and the transmitter powers are different, but fixed, for different frequencies. Our main observing site was at Hanscom Air Force Base (HAFB, 42.5°N, 288.7°E), MA, giving circuit lengths of 2820 km (WWV) and 490 km (CHU). WWV and CHU were chosen because they have protected frequency allocations, stability in frequency, and stability in power. Receive systems were also installed at Wallops Island, VA, and Bear Lake, UT, but those observations are not available for analysis.
 Routine observations were also made of the HF noise level in a nominal 3 kHz bandwidth, since it is the ratio of the signal power to the noise power (SNR) that is the main signal parameter determining the usability of a particular frequency for HF communications. Major broadband interferers severely limited our ability to detect weaker signals throughout the experiment.
 The main objective of this paper is to discuss the observed signal powers and the ability of the HF propagation programs Voice of America Coverage Analysis Program (VOACAP) and Advanced Stand Alone Prediction System (ASAPS) to predict the monthly median powers. Considerable care was taken to ensure the validity first of the measurement techniques, and secondly of the data analysis techniques. The observing interval of 10 months is too short to provide a definitive analysis of any propagation prediction program. For example, using monthly medians of the observations at a particular time and frequency results in maximum sample sizes of only 10. Valid medians could not be derived for those times at which the noise power was comparable to (or greater than) the signal power.
 Most of the previous comparisons of predicted and observed HF signal powers were made for long circuits with unknown propagation modes, using data banks established by CCIR. An exception to this was the set of observations made on a carefully engineered 1253 km circuit in Australia that was analyzed by Caruana  and provided the ground truth validation for ASAPS. The comparisons made under the auspices of CCIR were released as internal Working Group documents that are not generally available. Caruana  provides a list of these documents. The special value of the observations described here is that the circuits are simple midlatitude circuits with known equipment and reasonably well known one or two hop propagation modes.
Section 2 describes the receiving system, which was carefully calibrated. Section 3 describes the general background for the analysis procedure, while section 4 describes the important features of the data processing. Section 5 describes some of the observed powers, interpreting them in terms of known properties of the ionosphere. The accuracies of the predicted signal powers given by ASAPS and VOACAP are discussed in section 6. Because we do not have access to the contributions of the individual path loss terms given by each program, we are unable to interpret the differences between the results of the programs in terms of their different models of the major loss terms. Section 7 presents the conclusions of the paper.
2. ICOM Receiving System
 It is essential that observations of signal power be made with a carefully calibrated receiving system. The observations at HAFB were made using a system consisting of a calibrated antenna, a stable active preamp, and an ICOM PCR-1000 computer-controlled radio receiver. The system took 30 kHz spectra centered on each CHU/WWV broadcast frequency every 5 min, on a continuous basis. Observations were made of signal strength and noise level, which together provided the signal-to-noise ratio (SNR). The 30 kHz wide spectrum was chosen to allow cross comparisons to ionosonde receivers which have bandwidths of about this magnitude. The use of ionosonde receivers for monitoring purposes was also investigated during the campaign.
2.1. System Description
 The receiving antenna was a Passive Loop Antenna, PLA-1030/B, from Antenna Research Associates (ARA). The loop is a square with sides of 0.61 m, giving it a physical area of 0.372 m2. The receiving system at HAFB required two antennas because the antennas are directional, and the azimuths of the two transmitters differed by more than 30°. The antennas were set up on tripods that were set on the roof of a one-story shelter. The active preamps were connected to the antenna by ∼2 m of RG58 cable, which was then connected to an ICOM PCR-1000 receiver by 12 m of RG58 cable.
 In comparison to the pattern of a small loop antenna operating in free space, the ARA antenna patterns when operating above a real ground varied by less than about ±2dB across all eight frequencies when the incident wave's elevation angle was between 10° and 50°. 50o was the highest expected elevation angle for the propagation circuits. The patterns for the four frequencies are shown in Figure 1.
 As the elevation angle drops below 10°, the gain above real ground drops quickly, thus allowing for little or no signal to be detected below 5°, especially in a noisy environment. Because of the small variation of the gain across most angles, and the fact that the actual elevation of the incident radio wave is not measurable by this system, the real ground effects on the antenna's gain were not included in our analysis. As described later, we restricted the elevation angles to 6° for the comparison between VOACAP and ASAPS signal powers. Both versions of the antenna's patterns were simulated in the Numerical Electromagnetics Code NEC version 2, with the real ground modeled by a relative dielectric constant of 15 and a conductivity of 5.0 × 10−3 S/m.
 After the signal strengths are derived from the measured voltages, the spectrum of calibrated values is analyzed to produce the WWV/CHU signal level, noise level, SNR, and the strength of the maximum observed signal in the spectrum, along with qualifiers and error estimates. The WWV/CHU signal level is simply the strength of the signal observed at the carrier frequency in the center of the spectrum. The spectrum's noise floor is determined by averaging the signal levels of the spectrum's eight lowest bins. The SNR of the spectra is then the difference in log scale between the power of the CHU/WWV signal and the noise level.
2.2. HF Noise
 The HF noise observed at HAFB is both frequency- and time-of-day-dependent. It was not our intention to investigate the details of the HF noise, so we did not attempt to isolate the various noise sources, nor the reasons for the observed diurnal and seasonal variations. Our main concern with regards to the noise was how it affected the reliability of the signal power observations. In general, the frequency dependence of the noise is consistent with the Recommendation ITU-R P.372-8 [International Telecommunication Union, 2003] formula for the environmental HF noise, Ne(f) = N1 − G log10(f), where N1 is the noise density in dBW/Hz at 1 MHz, and G = 27.7. For a business site, N1 is −127.2, which fits the observations reasonably well.
3. Introduction to the Data Analysis
 The WWV transmitter is at Fort Collins, Colorado, at (40.7°N, 255.0°E). The transmitter power was 10.0 kW on 5, 10, and 15 MHz, and 2.5 kW on 2.5 and 20 MHz. The CHU transmitter is at Ottawa, Canada, at (45.3°N, 284.2°E). The power was 3 kW at 3.330 and 14.670 MHz, and 10 kW at 7.335 MHz. The Fort Collins–HAFB circuit is 2820 km in length, while the CHU-HAFB circuit is 490 km. For 1F propagation modes (i.e., the signals are reflected once from the F region), the elevation angles would be approximately 5° for the WWV circuit, and about 50° for the CHU circuit. The WWV antennas are vertical half-wave dipoles located 3/8 λ above good ground. The gain drops off sharply at low elevation angles, from a gain of −4 dB at the 1F takeoff angle of 5° to −10 dB at 2°. The theoretical antenna pattern is given by Viezbicke . The CHU transmitting antennas are also vertical, with gain patterns similar to the WWV pattern. These patterns were provided to us by J. d'Avignon (personal communication, 2004).
 We have chosen to compare two standard HF propagation prediction programs, ASAPS and VOACAP, using the monthly medians of the observed signal power. ASAPS was developed by the Australian IPS Radio and Space Services, and made available for scientific purposes to the authors. The basic physics used in ASAPS is described by Caruana . VOACAP is a Voice of America derivative of the program IONCAP that was developed by the Department of Commerce [see, e.g., Lane, 2001]. Goodman  provides an extensive background to the whole issue of HF propagation modeling for communications purposes.
 The major losses on an HF circuit are the inverse square losses due to the spherical spreading of the energy as the wave propagates, and the absorption of some of the energy as the signal passes through the D and lower E regions of the ionosphere. There is some potential for the ASAPS and VOACAP inverse square (or free-space) losses to differ because the programs use different methods of estimating the effective height of reflection, and of determining the elevation angles and propagation modes that contribute to the total received signal. The two programs also adopt very different models of HF absorption. ASAPS uses a model of HF absorption based on worldwide observations of vertical incidence absorption at a nominal frequency of 2.2 MHz [see George and Bradley, 1974]. The model agrees closely with the description given by Davies [1990, chapter 7]. The VOACAP absorption calculations, on the other hand, are based on the semiempirical model of Lucas and Haydon .
 HF signal powers are commonly expressed in units of dB above a watt (dBW), which is what VOACAP provides. ASAPS provides the field strength for each propagation mode in units of dB above a microvolt per meter, dBμ. The conversion between received signal power (P) and field strength (E) is given by [see, e.g., McNamara, 1994]
where the square brackets enclose the units for each term, and Gr is the gain for the receiving antenna. Gr was set to zero. The VOACAP runs were also made with a 0 dBi receiving antenna. A minimum angle of 3° was used for both programs. (A limit of 6° is actually applied in the later comparisons of the predicted and observed signal powers.)
Figures 2 and 3 give the VOACAP maximum usable frequencies (MUF) for the CHU and WWV to HAFB circuits for selected months in 2003. The ASAPS MUF curves are very similar. An operating frequency equal to the MUF at a particular hour would be supported on 50% of the days of the month. The frequencies analyzed were 3.330 and 7.335 MHz for CHU, and 2.5, 5.0, 10.0, 15.0 and 20.0 MHz for WWV.
 Propagation support was predicted on 3.330 MHz for each of the four months illustrated, for all 24 hours. 7.335 MHz support was predicted for January, March and September, but only during the day (about 1200–2400 UT). For the WWV circuit, 2.5 and 5.0 MHz support was predicted for all 24 hours. 10 MHz support is marginal between about 0800 and 1200 UT (0200 to 0600 LT at the circuit midpoint). 15 MHz support is predicted for all months during the daytime, while 20 MHz support is predicted for January, March and September (marginally).
 The MUF predictions simply indicate if the ionosphere would support the propagation, in terms of the electron densities being high enough. The highest MUFs thus occur during the middle of the day (around 1800 UT, or 1200 LT), and the lowest occur just before dawn. Whether or not the signals would be detectable depends on whether the signal power is sufficiently greater than the noise level at the receiver. In general (ignoring local noise sources), the HF noise from remote transmitters and thunderstorms is higher at the lower frequencies and at night. The signal power itself depends mainly on transmitter power and on the major loss terms, which are the inverse square path loss and the nondeviative absorption loss. The absorption loss is greatest at low frequencies and during the day. Thus low frequencies are heavily absorbed during the day, and such signals are overwhelmed by the noise. On the other hand, high frequencies do not suffer much from absorption, and the HF noise drops off with increasing frequency. However, such frequencies are reflected only when the electron densities are high enough, which is during the day.
3.1. Propagation Modes
 The dominant propagation modes (i.e., those with the highest field strength) are modeled by both ASAPS and VOACAP to be 1F, 2F and 2E on the WWV-HAFB circuit, and 1F and 1E on the CHU-HAFB circuit. Which propagation mode provides the highest field strength depends in part on the antenna pattern. In general, the 2F mode will be weaker than the 1F mode, because the 2F mode traverses the absorbing regions of the ionosphere 4 times (as against 2), and also loses energy at the intervening ground reflection. However, these extra losses can be overcome if the antennas have a higher gain at the 2F takeoff angle than at the 1F takeoff angle. For the WWV-HAFB circuit, the takeoff angles for the 1F and 2F modes are about 5° and 20°, respectively. The transmitting gain at 5° is 3 dB down on the gain at 20° [Viezbicke, 1971]. This is not usually enough of a differential for the 2F mode to be favored over the 1F mode, so on this basis we would expect the 1F mode to be the dominant mode. Like the 1F mode, the 2E mode also has a takeoff angle of ∼5° and is often the dominant mode predicted by ASAPS during the day on 10 MHz.
 ASAPS provides signal powers (actually signal strengths) separately for each of its modeled propagation modes, but in our comparisons of predicted and observed signal powers, we simply sum the powers (in watts, not dBW) from all supported modes. VOACAP provides only the total power for all propagation modes, but identifies the dominant mode.
3.2. Monthly Median Signal-to-Noise Ratios
 The most important aspect of the signal-to-noise ratios (SNR) is their influence on the reliability of the signal power observations. They are of operational interest because the SNR plays a key role in HF communications, but that is not the issue being addressed here. Observations for which the SNR did not exceed 3 dB have been excluded from the error analysis, as unreliable. Figures 4 and 5 show as examples the diurnal variation of the observed SNR for the CHU 3.330 and 7.335 MHz cases.
 For the 3.330 MHz signals, the SNR fails to exceed the 3 dB threshold between about 1300 and 2100 UT (0800 to 1600 LT) in several months. For the 7.335 MHz signals, the SNR fails to exceed the 3 dB threshold between about 0800 and 1200 UT (0300 to 0700 LT).
4. Data Analysis Procedures
 A set of observations was made on each frequency every 5 min. The receiving system scanned over 30 kHz surrounding each of the 5 WWV and then the 3 CHU frequencies for 18 s. It recorded the transmitter name, frequency, signal power, noise power and SNR, as well as the estimated uncertainties in each of these measurements. Since propagation prediction programs provide monthly median values, the observations have been assembled into month files that record the monthly median value of each of the signal power, noise power and SNR for each frequency and universal time hour. To start the data processing, the median value for the 11 observations made within 25 min of a UT hour was determined and attributed to that hour. The 30-min observation was ignored.
 By the nature of the measurement algorithm, there was always a value for each 5-min record. However, if the SNR did not exceed 3 dB, the signal observation was deemed to be unreliable, and replaced by the “no observation” value of −999. The median value was obtained by sorting the data into increasing order, and then taking the middle value as the median. The signal (and noise) powers are always less than zero. The strongest signals are therefore at the opposite end of the sorted array to the no-observation values (−999). Signal powers with SNR below 3 dB were implicitly assumed to lie below the median value of the signal power. Such cases could have corresponded to no propagation support, or to the noise being too high for a supported signal to be detected. Introducing the 3 dB SNR threshold could have the effect of excluding good data, but this is preferred to the alternative. The median values at each hour for all days of the month were then used to determine the monthly median value for that hour, again allowing for no-observation cases. Lower and upper decile values were also determined at this stage, although the lower deciles could not always be defined because of the no-observation cases.
 The automated signal recognition algorithm could not be guaranteed to be 100% accurate, especially in the case of weak signals. In the extreme case of a very weak signal, any “signal” detected by the algorithm would probably be noise. To avoid the inclusion in our analysis of signal powers contaminated by unrecognized noise, we have looked for any correlation between corresponding individual 5-min observations of signal and noise powers. Significant correlations would indicate that the supposed signals were in fact noise.
Figures 6 and 7 show, by way of example, the corresponding signal and noise power observations for WWV 2.5 MHz and 15.0 MHz signals, for January 2003.
 The oblique lines define Noise (N) = Signal (S). The clear area to the right of these lines corresponds to observations with SNR < 3dB, which have been rejected as unreliable.
 It is obvious that the S and N values are correlated on 2.5 MHz, making those observations useless (in fact, the correlation coefficient was r ∼ 0.7). On the other hand, the 15 MHz observations are basically uncorrelated (r ∼ 0.15). The relatively low noise values (−133 dBW) on 15 MHz were observed on New Year's day, 2003. The correlation coefficients between individual signal and noise observations have been calculated for each frequency and each month, separately for daytime and nighttime observations. Using a correlation coefficient of 0.5 as the cutoff, the 2.5 and 5 MHz daytime observations, and 2.5 MHz nighttime observations, are not considered as reliable in the present analysis. Thus the 2.5 MHz data was not considered further, apart from a very limited period. The 7.335 MHz observations did not present a simple case, because the correlation coefficients were low in only July and August. In some months, the propagation was not supported for the few hours before dawn.
5. Sample Observations
 This section presents some typical signal power observations, mostly in terms of the monthly median observed power in dBW for a fixed frequency versus universal time.
5.1. Mass Plots of Individual Data Points
Figure 8 shows an example of the individual (every 5 min) signal powers, with the monthly median powers superimposed, for CHU 7.330 MHz signals in March 2003.
 Observations with SNR < 3 dB are not included. The 5-min sampling interval of the observations means that they cannot be used to determine the fading characteristics of the signals, because the fading due to interference between propagation modes (Rayleigh fading) typically has a period of the order of a few minutes. However, the 5-min interval is quite sufficient for investigating the monthly median observed powers. Figure 8 shows that the derived monthly median powers are a good representation of the individual observations, while at the same time illustrating the large dispersion of the powers at a particular time.
5.2. CHU 3.330 and 7.335 MHz Propagation
Figures 9 and 10 show the diurnal variation of the monthly median observed signal powers in dBW on 3.330 and 7.335 MHz for the CHU Ottawa to HAFB circuit. There is one curve for each of the 10 months of the observing period. The “No signal observed” corresponds to signal-to-noise ratios of less than 3 dB.
 Because 3.330 MHz is a low frequency as far as HF absorption is concerned, it would not be expected to propagate very successfully during the middle of the day, especially in summer. At 1700 UT (noon), for example, propagation was observed only in March, April and May. After sunrise, and before sunset, but not including the middle of the day, propagation would be supported by the 1E mode with a takeoff angle of 45° to 50° (following ASAPS). The E layer would shield the F layer, and there would be no 1F propagation. In the middle of the day, both modes would be heavily attenuated.
 The 7.335 MHz observations at night (0000 to 1200 UT) are uncertain because the individual signal and noise powers are highly correlated, although the observations actually look quite reasonable (Figure 10). The observed powers at 7.335 MHz reach a minimum at ∼1100 UT, or 0600 LT (the LT at the circuit midpoint). The missing months between 0800 and 1200 UT (0300 to 0700 LT) are May, June, August and September. The daytime powers show a noon minimum characteristic of HF absorption. At noon, there are two groups of curves. The top group (stronger signals) includes January, February, March, September and October, while the lower group includes the summer months April through August. This is consistent with the cos χ dependence of absorption (greatest for an overhead sun, or χ = 0).
5.3. WWV 5 and 10 MHz Propagation
Figures 11 and 12 show the diurnal variation of the observed monthly median signal powers for the WWV Fort Collins to Hanscom Air Force Base on 5 and 10 MHz, respectively, for each month of the 10-month observing period. There is one curve for each of the 10 months of the observing period. The “No signal observed” corresponds to signal-to-noise ratios of less than 3dB.
 The 5 MHz observations present no surprises. The propagation is restricted to the night because low frequencies suffer from HF absorption, which is basically a daytime phenomenon. The daytime minimum in signal power at 10 MHz (Figure 12) occurs at 1800 UT, which is ∼1200 LT, and is clearly related to HF absorption. The highest midday signal powers occur in January and February, followed by March and April, which is again consistent with the known cos χ dependence of absorption. The diurnal variations for the other months are too close together to discern a clear trend.
5.4. Nighttime Dropout in 10 MHz Reception
Figure 12 showed a consistent and significant decrease in the 10 MHz signal power for all months except January, at around 0800 to 0900 UT (0200 to 0300 LT). On the other hand, both ASAPS and VOACAP show a smooth diurnal variation. For example, the observed power drops to −110 dBW in May at 0900 UT, whereas a smooth diurnal variation would have given a value of about −95 dBW. The simplest explanation for the discrepancy is that the circuit did not support the 1F propagation that is predicted by both ASAPS and VOACAP, at least not on a median basis.
Figure 13 shows the upper decile, median and lower decile values of the observed 10 MHz signal power for May 2003.
 The dip in the median observed power at 0800–1000 UT suggests that the 1F mode is not supported. This interval also corresponds to high numbers of observations with powers too low for the observation to be considered reliable (SNR < 3 dB). These counts reached 30% of the total. After making allowance for the noisy nature of decile values, it can be seen that the upper decile curve does not show the dip seen in the median curve at 0800 to 1000 UT. Thus the circuit does in fact seem to support the 1F mode on at least some days.
 It is possible that the propagation observed on those days that apparently did not support the 1F mode was via above-the-MUF propagation. Above-the-MUF propagation was investigated by M. L. Phillips and W. Abel in 1958. 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, the higher the signal strength. The received signal strength will of course be lower than for the normal F layer propagation mode. Phillips and Abel found that their predicted path losses agreed well with observations between Texas and New England. Above-the-MUF propagation is included in VOACAP but not in ASAPS.
6. Sample Comparisons of Observations and Predictions
 The comparisons of errors in the predicted signal powers that are presented here are all based on those times for which both programs predicted propagation support, and for which propagation was actually observed. We have not considered in any detail those situations in which only one program or neither predicted propagation, since there is no valid definition of “propagation not supported,” the SNR just gets smaller and goes below the system threshold. As described earlier, there are large uncertainties in the antenna gain calculations for low elevation angles. However, the uncertainties are acceptably small (less than ∼2 dB) for angles greater than or equal to 6°. We have therefore processed predicted powers only when the program (ASAPS or VOACAP) indicated an elevation angle greater than or equal to this angle. This has the effect of sometimes eliminating the low-angle one-hop propagation modes from the comparisons.
6.1. WWV 2.5 MHz Propagation
 Although the WWV 2.5 MHz observations are considered generally unreliable because of the high noise levels, some useful information can be obtained by careful analysis. For example, the correlation coefficients between individual signal and noise values for April and May are well clear of the acceptable level. Likewise, the SNR exceeds ∼8 dB between 0200 and 0800 UT, for all months except January, February and March. Table 1 shows the observed, ASAPS, and VOACAP signal powers for April and May, between 0100 and 0900 UT (1900 and 0300 LT). Zero values indicate no propagation predicted. There is not much variation of the powers with time of day. Taking the medians of each set of nine values shows that the ASAPS errors are about −5 dB, whereas the VOACAP errors are about −15 dB (i.e., underestimates).
Table 1. Observed and Predicted Median Signal Powers at 2.5 MHz, April and May 2003
6.2. WWV 10 MHz Propagation
 The ASAPS and VOACAP errors for 10 MHz propagation on the Fort Collins to HAFB circuit are shown in Figure 14. Note that the errors are plotted against local time. (Prediction programs use UT.) There is an ASAPS point for every VOACAP point, and points are plotted only if the SNR was greater then 3 dB.
 The ASAPS and VOACAP average errors have very similar diurnal variations, but different zero levels. The ASAPS errors are their closest to zero during the day and early evening. The errors are greatest between midnight and dawn. The VOACAP errors are their closest to zero at night. The VOACAP errors are greatest (largest underestimates) at noon. In general, the VOACAP RMS errors are larger than the ASAPS errors during the day, and lower during midnight to dawn. During the night, both programs indicate 1F propagation. During the day, the dominant ASAPS mode is 2E, while the VOACAP mode is 2F.
 Analysis of the ASAPS powers for the separate 1F, 2F and 2E modes with no cutoff angle shows that the small ASAPS errors between 0700 and 2300 LT correspond to the 2F mode at night and the 2E mode during the day. The 2F mode is not supported between midnight and dawn (according to ASAPS), which leaves the 1F mode as the only possible “normal” mode of propagation. ASAPS predicts support by the 1F mode, with powers of about −83 dBW, versus the observed powers of −95 to −110 dBW. The large overestimates by ASAPS at these times could mean that there is actually no 1F propagation, because the receiving antenna has in fact too low a gain at the low angles of propagation (∼6°). Propagation could then have been by above-the-MUF 2F propagation. VOACAP includes above-the-MUF propagation, and has an RMS error of only ∼5 dBW.
6.3. CHU 3.330 and 7.335 MHz Propagation
 The CHU-HAFB circuit is much shorter than the WWV-HAFB circuit (490 km versus 2820 km), so there is not much ambiguity regarding the propagation modes, and the predicted ASAPS and VOACAP powers should agree better. Figure 15 shows the errors in the ASAPS and VOACAP signal powers for 3.330 MHz propagation.
 The ASAPS and VOACAP errors are very similar for 3.330 MHz propagation, which is not supported during the middle of the day because of the very strong HF absorption. The errors for both programs have maximum values just after sunrise and just before sunset. This phenomenon is related to the appearance/disappearance of the E layer, and the switch between 1E and 1F propagation modes. It is very difficult to model such dynamic situations.
 At 7.335 MHz (Figure 16), the VOACAP errors are about ±2 dB, but the average ASAPS error is ∼6 dB. The 7.335 MHz observed power at night was considered unreliable, so no comparisons are made at this time.
 One of the aims of the present study was to determine which of the two programs, ASAPS and VOACAP, gave the more accurate predictions of monthly median signal power, for the circuits and frequencies observed. In fact, neither program is clearly better than the other.
 Before any comparisons are drawn, it should be noted that:
 1. The maximum sample size is 10, the number of months considered.
 2. Some of the errors in the predicted powers may be due to the assumption that propagation always occurs via “normal” modes. The possibility of sporadic E modes is not specifically considered.
 3. We have processed predicted powers only when both programs indicated an elevation angle greater than or equal to 6°.
 There are several situations with clear differences between the errors (not all have been discussed above):
 1. The ASAPS errors are less than the VOACAP errors for 2.5 MHz WWV-HAFB propagation, for a limited range of UT and month during which the observed powers can be considered to be reliable (−5 dB versus −15 dB). See Table 1.
 2. The ASAPS RMS errors are less than the VOACAP RMS errors for 5 MHz WWV-HAFB propagation during the night (by 5 to 15 dB).
 3. The diurnal variations of the ASAPS and VOACAP errors for 10 MHz propagation are very similar, with neither program always being the more accurate. See Figure 14.
 4. The VOACAP errors are less than the ASAPS errors for 15 MHz WWV-HAFB propagation (during the day). The VOA errors are about +7 dB, while the ASAPS errors are about 15 ± 5 dB.
 5. The VOACAP errors are less than the ASAPS errors for 20 MHz WWV-HAFB propagation (during the day). The VOACAP errors are a few decibels, while the ASAPS errors are about 15 ± 5 dB.
 6. The VOACAP errors (RMS error ∼4 dB) are less than the ASAPS errors (RMS error ∼8 dB) for 7.335 MHz CHU-HAFB propagation during the day. (The errors for the two programs are very similar for 3.330 MHz propagation.) The individual errors are given in Figures 15 and 16.
 For the long WWV circuit, ASAPS is the more accurate for the lower frequencies (at night), while VOACAP is the more accurate for the higher frequencies (during the day). There is no systematic difference between the programs for the 10 MHz powers. Neither program is successful at reproducing the detailed seasonal variations of the observations at any frequency.
 As well as the possibility of above-the-MUF propagation, there are other unknowns that have affected the present analysis. Key among these is the lack of elevation angle measurements, which would help to determine the propagation mode. A related issue is that it is very unwise to expect that the same mode would be supported on a multimoded circuit, hour after hour. Angle of arrival observations [McNamara, 1991] have shown quite clearly that each of the supported modes take turns at being the strongest mode, as the other modes fade down.
 Comparisons of signal powers predicted by programs such as VOACAP with a large CCIR database of observations revealed that the programs generally overestimated the received powers, typically by ∼9 dB at midlatitudes. VOACAP therefore includes an adjustment of ∼9 dB known as “the excess system loss” that is subtracted from the predicted powers. ASAPS does not include this term. It is interesting to note that the VOACAP errors at night on 2.5 (Table 1) and 5.0 MHz would be decreased to the size of the ASAPS errors if the VOACAP powers were increased by 9 dB. However, the 10 MHZ errors at night would then increase.
 The VOACAP runs were made by George Lane. We would like to thank him for his willing cooperation and for sharing his invaluable practical experience with us. We would also like to thank Steven Best of the AFRL Sensors Directorate, Antennas Branch, Hanscom Air Force Base, for his help in developing our antenna calibration scheme. The program ASAPS was made available to the authors by IPS Radio and Space Services, Sydney, Australia. John Caruana provided valuable support during our analysis of the observations.