CCIR Report 322-3 defines these parameters as follows:
sFam Standard deviation of Fam
Fam Median of the hourly values of Fa within a time block
Fa Effective antenna noise figure (F = 10 log f)
fa Effective antenna noise factor that results from the external noise
power available from a loss-free antenna
Du Upper decile, value of the average noise power exceeded 10% of
the hours within a time block (dB above the median value for the
time block)
Dl Lower decile, value of the average noise power exceeded 90% of
the hours within a time block (dB below the median value for the
time block)
sDu The standard deviation of Du
sDl The standard deviation of Dl
The first part of this technical document describes the methods that National Bureau of Standards (NBS) researchers originally used to calculate the predicted CCIR noise variation parameters from the measured data.The remainder of this document gives suggestions for interpreting and using the CCIR Report 322 noise variation parameters.
The researchers calculated the median value and upper and lower deciles for each time block based on the 360 hourly noise samples taken per year. This document designates these as FMam, DMu, and DMl. The capital M distinguishes parameters directly calculated from measured data from the predictions given in CCIR Report 322, which are designated as Fam, Du, and Dl.
Researchers originally generated each 1 MHz contour map using the following two steps:
Figure 2. Noise contour variation with frequency.
Researchers generated the associated Frequency Variation Charts in CCIR Report 322 by a form of constrained least squares fit of the eight implied maps in figure 2 (one map for each measurement frequency) to the measurement data points associated with each map. The curves on the Frequency Variation Charts were computed during least squares mapping as documented in NTIA Report 85-173 (Spaulding & Washburn, 1985, p. 106):
where Ai(z) = Bi,1 + Bi,2z, i=1,7
and 
and where f is the desired frequency in MHz.
(This mapping was subject to the constraint Fam(-0.75,z) = z i.e., the 1-MHz values must equal z)
The root-mean-square (rms) average of the deviations of the measured data points from the predicted noise values (Fam) at these measurement points (after translation by the Frequency Variation Chart), on each of the implied maps in figure 2, is the value of sFam given in CCIR Report 322 (International Telecommunications Union, 1963). There is one value of sFam for each implied map and its associated frequency. The CCIR Report 322 chart plots this parameter (and others) as a function of frequency by drawing a smooth curve through the values of sFam calculated in this way for each of the eight measurement frequencies. According to Spaulding and Washburn (1985, p. 135), the smooth curves are of the following form:
Although not covered in detail in this technical document, CCIR Report 322 researchers calculated the values of Vdm and sVd using the same methods that they used to calculate the upper and lower deciles and their associated standard deviations.
The following factors may affect communication system performance, but are not covered in this technical document.
Note that CCIR Report 322 assumes that the probability distribution of each noise and signal variation parameter is log-normal. When the parameter is expressed in dB it will be the well-known, normal distribution.
For either approach to using the CCIR noise variation parameters, researchers calculate the expected value of the signal-to-noise ratio (SNR) in dB as the difference between the expected signal level (in dB) and the expected noise level (in dB). They obtain the expected signal value from propagation calculations not addressed in this document. The expected noise value is the predicted median noise level from CCIR Report 322 (Fam).
where 
The associated cumulative distribution is:
where PTA(DTA) is the time availability probability corresponding to a deviation from Fam of DTA
which can also be expressed as follows using the standard normal deviate (t) that is readily available via software routines and tables:
where 
and t(P) is used to represent the inverse of this function (standard normal deviate associated with cumulative probability P)
A useful expression for calculating the DTA corresponding to a time availability of PTA when the associated standard deviation is sTA can be written as follows:
Note that Dl is normally not used except when estimating receive systems' sensitivity requirements. Researchers combine all of the other variation parameters into a single prediction uncertainty parameter (random variable DSP, the deviation from Fam due to prediction uncertainties, used in CCIR Report 322 (International Telecommunications Union, 1963) examples, to determine the "service probability." The researchers assume that this prediction uncertainty parameter has the following log-normal probability distribution (because all of the parameters on which it is based are assumed to be log-normal, with the dB values of the contributing errors adding):
where
where 
is the standard deviation of the signal level prediction
is the standard deviation of the required signal to nosie ratio
is the standard deviation of Fam from CCIR-322
is the standard deviation of Du from CCIR-322
is the standard normal deviate corresponding to the cumulative probability, PTA
The associated cumulative distribution is:
where PSP(DSP) is the prediction uncertainty probability corresponding to a deviation from Fam of DSP
Again, this can also be expressed using the standard normal deviate (t), but in this case with:
A useful expression for calculating the DSP corresponding to a time availability of PSP when the associated standard deviation is sSP can be written as follows:
In the equation for sSP, sS represents the standard deviation of the signal-level prediction instead of the sp used in an example in CCIR Report 322-3 (International Telecommunications Union, 1968). The values of sS associated with NRaD VLF/LF signal predictions cannot be easily broken apart into separate time availability and prediction uncertainty components. Therefore, this standard deviation is a mixture of these two components. Because of this, working with a separate sSP and sTA appears to not be a useful way of viewing the uncertainties associated with NRaD VLF/LF propagation predictions (even though this is the approach implied by the CCIR Report 322 examples). Combining them into a single overall standard deviation, as discussed in section 3.1.2, appears to be the best approach.
Also, for the VLF predictions done at NRaD, researchers currently give sR a zero value because field measurements show that the Navy's current VLF receive systems are fairly insensitive to the Vd parameter of atmospheric noise. In the CCIR Report 322 (International Telecommunications Union, 1963) example, researchers used the standard deviation of Vd to estimate a value to use for sR. Also note that the reason sDu is divided by 1.28 and then multiplied by t(PTA) in the expression for sSP is to scale it to the appropriate standard deviation that corresponds to PTA. This follows the approach implied by figure 28 in CCIR Report 322-3 (International Telecommunications Union, 1968).
So far, this section has specified two log-normal distributions:
or
Table 1. Cumulative probability points of the standardized
normal random variable.
The following equation is an example of this type of calculation for a time availability of 95% and a prediction uncertainty of 99%. The SNR that can be achieved with a 95% time availability would be the expected value of SNR, designated as SNR(50%, 50%), minus 1.64 times sTA, where the 1.64 factor was read from table 1. However, this still leaves only a 50% probability (confidence) that this 95% time availability will be achieved (because of the uncertainties associated with the prediction process). To improve this prediction confidence to 99%, researchers would subtract an additional term from SNR(95%, 50%), which was just calculated. This term would be 2.33 times sSP, and the result would be designated SNR(95%, 99%). The expression for these calculations is as follows:
Researchers can then describe the uncertainties associated with SNR(95%, 99%) as follows: "For the location, season, time, etc. of this prediction, we will have a SNR greater than or equal to SNR(95%, 99%) for 95% of the days of the season with a prediction confidence of 99%." CCIR Report 322 (International Telecommunications Union, 1963) refers to this prediction confidence as "Service Probability." One way of describing this prediction confidence (assuming there were no time variation components in sSP) is to say that "for 99% of the geographic points on the world map, for this season and time block, the actual SNR will be large enough to provide the specified time availability (95% time availability in this example)." The prediction uncertainty term could also be thought of as a "safety factor," applied to make sure prediction uncertainties do not prevent meeting the predicted time availability.
where 
and
where 
is the standard deviation of the signal level prediction
is the standard deviation of the required signal to nosie ratio
is the upper decile value from CCIR-322
is the standard deviation of Fam from CCIR-322
is the standard normal deviate of Du from CCIR-322
See the previous section for more details on sTA and sSP. In the expression for sSP, t(PTA) has been set to a value of one to account for the use of the Du term as a standard deviation (Du/1.28). The above calculation specifies a single log-normal distribution (random variable DOV with standard deviation sOV) of the overall variation of the SNR predictions around the predicted expected value of SNR. DTA and DSP are assumed to be independent log-normal random variables. Researchers can use table 1 again to find the factor needed to calculate the term to achieve a desired overall confidence level. The general expression for calculating the SNR for a desired overall availability is as follows:
or
The following expression is an example. The SNR that can be achieved with an overall availability level of 90% (designated as SNR(90%)), would be the expected value of the SNR (50% confidence level) minus 1.28 times sOV, where the 1.28 factor was read from table 1. The expression for these calculations is as follows:
This confidence level means that for the season and time block of this prediction, 90% of the measured values will be greater than or equal to the corresponding predicted SNR(90%), when calculated over both day of the season and all geographic locations on the world map.
If researchers must calculate the overall availability when the SNR margin above a receiver "good copy" threshold is known, straightforward use of the cumulative standard normal distribution will provide the corresponding overall confidence value directly from the value of the margin after being normalized by dividing it by sOV (see table 1 for a number of points in this cumulative distribution).
In the calculations of the overall uncertainty probability distribution, researchers assume the log-normal distribution for time variability (random variable DTA with standard deviation sOV) to be a symmetrical log-normal distribution with a standard deviation of Du/1.28. Generally, it is not symmetrical because in CCIR Report 322 (International Telecommunications Union, 1963), Du specifies the positive half of the distribution and Dl specifies the negative half of the distribution. Since Du does not necessarily equal Dl, this distribution is not necessarily symmetrical. Because of this asymmetry, the probability distribution of DTA is not exactly a log-normal distribution. However, the impact on the overall confidence level term is not very significant for the following reasons.
It may be desirable to combine this predicted time variation of the expected SNR with the associated CCIR-derived variability parameters to produce an overall time availability or overall general availability number.
Researchers can do this by calculating the probability of exceeding the "good copy" SNR threshold of the receiver system for each half-hour of the day (and each geographic point of interest). They use the variability parameters discussed earlier to specify the appropriate log-normal probability distributions needed to calculate this probabilty.
Now researchers can combine the probabilities of exceeding the receiver threshold associated with each half-hour by averaging them over the day (48 probabilities, one for each half-hour). This calculation results in either an overall time availability at a fixed service probability for the day, or an overall availability number for the day, depending on whether the researchers used sTA and sSP, or just sOV to specify the log-normal distribution(s). If the researchers desire a number representing the expected number of hours of coverage per day, then they should multiply this overall availability probability by 24 (the number of hours per day).
Figure 3. CCIR 322 noise parameters, winter, 30 kHz.
Figure 4. CCIR 322 noise parameters, spring, 30 kHz.
Figure 5. CCIR 322 noise parameters, summer, 30 kHz.
Figure 6. CCIR 322 noise parameters, autumn, 30 kHz.
Table 2. CCIR-332 (& CCIR332-3) statistical parameters (at 30 kHz).
SIGdu/1.28 and SIGdl/1.28 are both significantly smaller than the other noise variation parameters. Because of this, when SIGdu/1.28 is combined with Du/1.28 and SIGFam in the square root of sum of squares equation to arrive at the standard deviation of the overall variation (SIGov), it has a relatively minor effect on the value of SIGov. The calculation of SIGov for these charts does not include the signal-level variation parameter sS or the required SNR variation parameter sR, which were described earlier in this report. For a complete picture, researchers would need to combine these two standard deviations with SIGov using the square root of sum of squares formula. Also, the reason SIGdu is divided by 1.28 is to scale it to the appropriate standard deviation that corresponds to Du/1.28. This agrees with the approach implied by figure 28 in CCIR Report 322-3 (International Telecommunications Union, 1968). This comment also applies to SIGdl.
Time blocks have units of local time (LT). This is the convention used in CCIR Report 322 (International Telecommunications Union, 1963) and CCIR Report 322-3 (International Telecommunications Union, 1968). At first it may seem unusual that each noise contour map (and its associated table of noise variation parametrs) is for a single local time block over the whole world, i.e., 8 to 12 (LT) at every point on the surface of the earth. This approach gives the needed noise predictions correctly, as long as this detail is considered. Drawing the contours using this local time convention gave better accuracy. Apparently, this was because there was not as much difference in the noise levels recorded at a single local time at every point on the earth (thunderstorm activity is usually correlated with local time) when compared to using a single universal time (UT) where local times vary as they do in the real world. The associated chart of noise variability parameters (such as Du) is also for local time blocks. Note that this means that the averaging process used to compute these noise variation parameters is also based on measurements over the entire world taken at the same local time (not at the same universal time) and season.
Dave Niemoller, Science Applications International Corporation, presented an interesting method at the Fifth Office of Naval Research Workshop on ELF/VLF Radio Noise (Physical Research, Inc. for ONR, 1990). See appendix A for viewgraphs from his 1990 ELF/VLF Radio Noise presentation. Mr. Niemoller used the interpolation method presented at this workshop for interpolating between the time blocks (e.g., to get hourly Fam values instead of just 4-hour time block values). This method preserves the time block Fam values (when a number of evenly spaced interpolated values within a time block are averaged), and can also estimate the reduction in Du attributable to the change with time of the finer (interpolated) Fam values. Note that since Du is an average over all points on the world map, this estimated reduction in Du should have been based on an average over the world map of these estimated reductions. This is because the range of noise level variation is different at different spots on the surface of the earth. This interpolation method could probably also be applied to interpolating between seasons (e.g., to get monthly Fam values instead of just seasonal values). Mr. Niemoller has computer programs written in FORTRAN that implement his interpolation method.
Figures 7 through 16 are plots of Fam vs. (local) time block and of Fam vs. season for the following locations:
20N, 60W (near Puerto Rico)
60N, 30W (between Iceland and Greenland)
35N, 30E (East Mediterranean)
The range and character of the variations are differnt for different locations. The figures also show the size of the jumps in Fam from time-block to time-block and from season to season. Table 3 is the spreadsheet with the data on which figurs 7 through 16 are based.
Figure 7. CCIR 322 noise levels for three different locations, winter, 30 kHz.
Figure 8. CCIR 322 noise levels for three different locations, spring, 30 kHz.
Figure 9. CCIR 322 noise levels for three different locations, sumer, 30 kHz.
Figure 10. CCIR 322 noise levels for three different locations, autumn, 30 kHz.
Figure 11. CCIR 322 noise levels for three different locations, time block: 0
to 4 LT, 30 kHz.
Figure 12. CCIR 322 noise levels for three different locations, time block: 4
to 8 LT, 30 kHz.
Figure 13. CCIR 322 noise levels for three different locations, time block: 8
to 12 LT, 30 kHz.
Figure 14. CCIR 322 noise levels for three different locations, time block: 12
to 16 LT, 30 kHz.
Figure 15. CCIR 322 noise levels for three different locations, time block: 16
to 20 LT, 30 kHz.
Figure 16. CCIR 322 noise levels for three different locations, time block: 20
to 24 LT, 30 kHz.
Table 3. CCIR-332-3 values of Fam for three locations: 20N, 60W; 60N, 30W; 35N, 30E
(noise level at 30 kHz in a bandwidth of 1 kHz, local time)
Buckner, R. P., and S. M. Doghestani. 1993. "Improved Methods for VLF/LF Coverage Prediction," PSR Report 2380. Pacific Sierra Research Corporation, Santa Monica, California. Prepared for Office of Naval Research, Arlington, Virginia.
Defense Nuclear Agency. 1990. "Combined Threat Effects WABINRES VLF/LF Coverage Prediction." TR90-19. Washington, DC.
Defense Nuclear Agency. 1991. "TACAMO Pacific Area VLF/LF Communications Effectiveness," TR91-35. Washington, DC.
International Telecommunications Union. 1968. "Characteristics and Applications of Atmospheric Radio Noise Data," CCIR Report 322-3. Comité Consultatif International Des Radiocommunications, Geneva, Switzerland.
International Telecommunications Union. 1963. "World Distribution and Characteristics of Atmospheric Radio Noise," CCIR Report 322. Documents of Xth Plenary Assembly. Comité Consultatif International Des Radiocommunications, Geneva, Switzerland.
International Telecommunications Union. 1959. "Revision of Atmospheric Radio Noise Data," CCIR Report 65 (Revised). Documents of IXth Plenary Assembly (Volume III, p. 223). Comité Consultatif International Des Radiocommunications, Geneva, Switzerland.
Physical Research, Inc. for the Office of Naval Research. 1990. Summary Report of the Fifth ONR Workshop on ELF/VLF Radio Noise. 23-24 April 1990, Naval Ocean Systems Center (NOSC), San Diego, CA.
Spaulding, A. D., and J. S. Washburn. 1985. "Atmospheric Radio Noise: Worldwide Levels and Other Characteristics," NTIA Report 85-173. U.S. Department of Commerce, National Telecommunications and Information Administration, Boulder, Colorado.
