Using High Frequency Propagation to Calculate Basic Maximum Usable Frequency

Israa Abdualqassim Mohammed Ali

REVIEW 4 major objections 5 minor 8 references

Using High Frequency Propagation to Calculate Basic Maximum Usable Frequency

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A fitted, month-specific correction factor brings IRI's predicted maximum usable frequency into line with observations at a mid-latitude station during a sunspot maximum.

desk verdict The paper's only new element, a quadratic correction for 2001, is fitted and evaluated on the same data, so the reported error reduction is an in-sample artifact; the rest is a routine IRI validation exercise. read the letter →

arxiv 1908.01836 v1 pith:FYCOSOIV submitted 2019-08-05 physics.space-ph

Israa Abdualqassim Mohammed Ali This is my paper · ORCID

classification physics.space-ph

keywords ionospherefoF2M3000F2BMUFIRImodelmaximumusablefrequencysunspotcycleHFpropagation

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Basic maximum usable frequency (BMUF), the highest HF radio frequency that can be used between two points via the ionosphere, is commonly estimated from the International Reference Ionosphere (IRI) model. Comparing monthly medians at Wakkanai, Japan, this paper finds that IRI's BMUF tracks observed values well during low solar activity (2004, 2005) but systematically misses them during the high-sunspot year 2001. The paper fits a quadratic correction factor in local time, separately for each month, and shows that applying it reduces the mean absolute BMUF error from about 6–13 MHz to about 1–3 MHz. The claim matters because reliable MUF predictions during solar maxima are exactly what HF link planners need.

What carries the argument

The load-bearing object is the correction factor $C(t) = a_0 t^2 + a_1 t + a_2$, a month-specific quadratic polynomial in local time $t$, applied as a multiplicative factor to the IRI-predicted BMUF (which itself is $foF2 \times M(3000)F2$). The paper fits the three coefficients per month to the observed-minus-predicted ratio using all 24 hourly monthly-median values of 2001, then applies the factor across the whole daily curve. Because the observed error pattern is smooth in local time, the quadratic is able to flatten it to roughly 1–3 MHz residual error.

What would settle it

Apply the published monthly correction coefficients to IRI predictions for a different high-sunspot year (e.g., 2000 or 2002) at Wakkanai, or to a second mid-latitude station; if the corrected predictions no longer match observations, the 2001 agreement was an in-sample fit rather than a discoverable systematic bias.

Watch

Extended reading notes

Core claim

The paper's central claim is that the discrepancy between IRI-predicted and observed BMUF at Wakkanai in 2001 is not random scatter but a systematic, smoothly varying function of local time, with a different shape in each calendar month. The evidence is that a quadratic polynomial correction--coefficients $a_0, a_1, a_2$ listed for all twelve months--reduces the average absolute error from roughly 6 to 13 MHz to roughly 1 to 3 MHz across the 24 hourly bins. For low-sunspot years 2004 and 2005, no such correction is needed: observed and predicted BMUF tracks already agree except for a few months (January, September, December of 2004). For the F2-layer critical frequency $foF2$, IRI predictions correlate well with observations in all three years except January of 2001 and 2004. The author takes this as evidence that the model's high-sunspot BMUF bias at this mid-latitude station is a stable, correctable error in IRI's F2-layer representation.

Load-bearing premise

The whole correction rests on the Wakkanai monthly medians being accurate and complete, and on the 2001 residual pattern being a stable systematic error rather than noise, because the same year's data are used both to fit the correction and to demonstrate that it works.

Editorial extensions

If this is right

For low solar activity years, IRI's BMUF predictions at this latitude can be trusted without correction.
For high solar activity years, the BMUF error is systematic in local time and month rather than random, so it can be captured by a compact per-month quadratic function.
Applying such a correction would give HF link planners a simple way to improve frequency selection during sunspot maxima at mid-latitudes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

Because the correction is fitted and evaluated on the same 2001 data, the post-correction errors are likely optimistic; an out-of-sample test on 2000 or 2002 would show how much of the improvement is a real systematic bias rather than in-sample fitting.
The paper does not separate BMUF into its foF2 and M(3000)F2 contributions; if the high-sunspot bias originates mainly in one of these parameters, a more physical correction could target that parameter directly.
The fitted coefficients vary fairly smoothly from month to month, so a future study could parameterize them by sunspot number and provide corrections for arbitrary solar activity levels at mid-latitudes.
Repeating this fitting approach at other ionosonde stations would reveal whether the high-sunspot BMUF bias is local to Wakkanai or a broader feature of the IRI model at mid-latitudes.

Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Quick take: the central correction result is an in-sample fit, so the paper doesn't show what it claims. That said, the underlying data comparison is legitimate and the figures are clear enough to follow.

What's new: not much. The MUF relation is standard; comparing IRI foF2 and BMUF with ionosonde medians at Wakkanai for 2001, 2004, and 2005 is a routine validation exercise, and the paper cites several earlier IRI validation studies. The only novel piece is the quadratic correction for 2001, and that's where the trouble is.

The correction coefficients (Table 2) are fitted to the observed-minus-predicted residuals for each month of 2001. Table 4 then reports the absolute error between observed and this corrected prediction for the same 24 hours and same months. With three free parameters per month and 24 points, the error reduction from roughly 6–13 MHz to 1–3 MHz is mathematically guaranteed. It tells you nothing about whether the bias is a stable, correctable function of local time. There is no hold-out year, no different station, not even a held-out set of hours. No error bars on coefficients, no statistical test.

The 'good correlation' statements are also unsupported—no correlation coefficients, no RMS, no significance tests. And the text contradicts itself: the abstract says foF2 is an exception in January of 2001 and 2004, while the results section says good correlation for all 12 months. Figure 6 has an April panel labelled March, and Figure 9 repeats July for both July and August. These are not fatal to the data, but they signal the manuscript has not been carefully checked.

The biggest soft spot is the in-sample evaluation. Even if the Wakkanai medians are perfect, the correction is just an interpolation of the residuals. To make the claim stick, the author would need to apply the fitted coefficients to independent data—say 2002 or another station—and show the error stays low.

Who is this for? Someone who wants a quick look at how IRI does at one mid-latitude station during a high-sunspot year. It is not a methods paper and it does not advance the field. My recommendation: desk reject in current form. If the author redoes the validation properly, it could become a minor data report, but as submitted it should not go to review.

Referee Report

4 major / 5 minor

Summary. The manuscript compares observed and IRI-predicted monthly medians of foF2 and BMUF at Wakkanai for 2001 (high SSN) and 2004/2005 (low SSN). It reports generally good agreement for foF2 and for BMUF in low-SSN years, but poor agreement for 2001 BMUF. A quadratic correction (Eq. 1) with month-specific coefficients (Table 2) is fitted to the 2001 data; Table 4 and Figure 9 show that the corrected BMUF values are much closer to observed values. The paper concludes that IRI's high-SSN BMUF predictions can be corrected using this fitting technique.

Significance. If the correction were validated on independent data, it would be of modest practical value for HF frequency planning at mid-latitude stations during high solar activity. However, the paper's central claim is not established: the correction is fitted to the same 2001 data on which it is evaluated, so the error reduction in Table 4 is an in-sample artifact rather than evidence of a stable, reproducible IRI bias. The absence of quantitative agreement metrics, error analysis, and out-of-sample tests means the conclusions are not supported by the evidence presented.

major comments (4)

[Section 3, Eq. (1), Tables 2-4, Figure 9] The correction procedure is circular. Equation (1) with the Table 2 coefficients is obtained by fitting the observed-minus-predicted residuals of 2001, and Table 4 and Figure 9 then show the corrected values on the very same 2001 data. With three free parameters per month and 24 hourly points, a least-squares fit necessarily reduces the in-sample residuals, so the improvement from roughly 6-13 MHz (Table 3) to 1-3 MHz (Table 4) is guaranteed by construction. The abstract's claim that predicted BMUF 'can be corrected' is therefore an interpolation statement, not a demonstrated predictive correction. The paper provides no validation on an independent year, station, or held-out hours, and no statistical test distinguishing the correction from a fit to noise.
[Section 4, Figures 3-8, Table 3] The claim of 'good correlation' is not quantified anywhere. No correlation coefficients, RMS errors, or confidence intervals are reported, yet the paper draws conclusions about agreement from visual inspection of the figures. For example, Table 3 lists absolute errors as large as 28.5 MHz for December 2001, which is inconsistent with the text's characterization of the 2001 BMUF comparison as merely 'bad correlation' without further detail. A quantitative metric is needed to support the 'good/bad correlation' taxonomy used throughout.
[Abstract vs. Section 4] There is an internal contradiction about the January exception. The abstract states that foF2 shows good correlation 'except for January of years 2001 and 2004,' while Section 4 states that there is good correlation 'for all 12 months and year chosen.' Similarly, the abstract lists months 1, 9, and 12 of 2004 as exceptions for BMUF, but Section 4 says there is good correlation 'for all 12 months when SSN low.' The reader cannot determine which claim is intended, and this ambiguity affects the paper's conclusions about model performance.
[Section 2, Data Selection] The reliability of the observed data is not established. The analysis uses monthly medians from the Wakkanai ionosonde, but there are no completeness statistics (number of days per month), no quality-control flags, no estimates of observational uncertainty, and no discussion of data gaps. Since the fitted correction and the error tables are built directly on these medians, missing or poor-quality data would directly bias the fitted coefficients and the reported error reductions. The paper should document data availability, median calculation procedures, and a measure of data quality.

minor comments (5)

[Figures 4, 6, and 9] Several figure panels are mislabeled: Figure 4 repeats the 'Jul\2004' label (the second July panel should be August), Figure 6 includes a panel labeled 'Mar\2001' twice (the fifth panel appears to be May), and Figure 9 repeats 'Jul\2001' (the second July panel should be August). These mislabels make it difficult to interpret the results.
[Section 3, Eq. (2)] Equation (2) is never defined, referenced, or used in the text; it should be removed or explained.
[Table 2] The coefficients are given with inconsistent precision (e.g., -0.006 vs. -2E-05); they should be reported with a common number of significant digits.
[Tables 3 and 4] The table headers do not state the units of BMUF; the text uses MHz, but the tables should be explicit about units.
[References] The reference list is incomplete: the 'Harris (2005)' entry lacks the full author list, and 'Nagar et al. (2015)' appears to contain PACS numbers rather than a journal citation.

Circularity Check

1 steps flagged · score 6.0 of 10

Correction coefficients are fitted to the 2001 residuals and then evaluated on the same 2001 data, so the reported error reduction is an in-sample fit-quality measure, not a validated prediction.

fitted input called prediction [Section 3 'DATA ANALYSES' (eq. 1, Table 2, Tables 3-4, Figure 9)]
"it can be corrected by fitting taken correction formula (eq. 1) for 24 hour. Table 2 represents the fitting coefficients a0, a1, and a2. Tables 3 and 4 reveal the absolute error between observation and prediction values before and after correction respectively for 24 hours and 12 months for year 2001."

The coefficients a0, a1, and a2 in Table 2 are obtained by fitting equation (1) to the observed-minus-predicted BMUF residuals of 2001, and Table 4 / Figure 9 then show the 'corrected' values on the same 24 hourly medians per month used in the fit. With three free parameters per month and 24 data points, a least-squares fit must reduce in-sample residuals; the drop from Table 3 to Table 4 is therefore guaranteed by construction and is a measure of fit quality, not evidence that IRI's high-sunspot BMUF error is a smooth, reproducible function of local time. No held-out year, station, or hours are used to validate the correction, and no coefficient uncertainties or significance tests are provided.

full rationale

The paper's foF2 comparisons and the low-sunspot BMUF comparisons (2004, 2005) are externally benchmarked against observed ionosonde monthly medians; those parts are self-contained and not circular. The circularity is confined to the high-sunspot 2001 BMUF correction, which is the central new result. The correction polynomial in equation (1) is fitted to the 2001 predicted-minus-observed residuals, and the subsequent 'after correction' errors in Table 4 and the agreement in Figure 9 are computed on the identical 24 hourly medians used for the fit. With three fitted parameters per month, the error reduction is an in-sample artifact and cannot establish that IRI's high-sunspot BMUF bias is correctable in any predictive sense. There is no independent validation on a different year, station, or held-out subset, and no error bars on the fitted coefficients. The conclusion that the predicted BMUF for 2001 'can be corrected' is therefore, by the paper's own procedure, equivalent to fitting the same data it then displays as corrected. This warrants a score of 6: the central correction claim reduces by construction, while the rest of the comparison study retains independent content.

Assumptions & free parameters 1 free parameters · 4 assumptions · 0 invented entities

The central comparison uses IRI as a reference prediction and the standard MUF formula; the only newly fitted quantities are the monthly correction coefficients, which are fit to the data they later correct.

free parameters (1)

Monthly quadratic correction coefficients a0, a1, a2 = 12 sets of three coefficients listed in Table 2
Fitted to the 2001 observed-predicted BMUF residuals; they fully determine the corrected values and are the only quantities introduced by the analysis.

assumptions (4)

domain assumption IRI model predictions with CCIR coefficients are realistic foF2 and M(3000)F2 values for Wakkanai.
The entire comparison depends on IRI being a valid reference for the stated periods.
standard math MUF = foF2 * M(3000)F2 is a valid formula for Basic Maximum Usable Frequency.
Standard ionospheric propagation formula cited from the literature.
domain assumption Monthly medians of daily ionosonde values are representative for each hour.
The paper computes monthly medians without discussing data completeness or outliers.
domain assumption The IRI-CCIR run used the correct coefficient sets for the given station and dates.
No IRI version, options, or input details are provided, yet model output is treated as authoritative.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Using High Frequency Propagation to Calculate Basic Maximum Usable Frequency." pith.science (2026). https://pith.science/paper/FYCOSOIV

@misc{pith2026190801836,
  author       = {Pith},
  title        = {Pith review of: Using High Frequency Propagation to Calculate Basic Maximum Usable Frequency},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FYCOSOIV}},
  note         = {Machine review of arXiv:1908.01836}
}

abstract

A comparison between observed (obs.) digital ionospheric sounding data and predicted (pre.) using International Reference Ionosphere (IRI) model for critical frequency (foF2) and Basic Maximum Usable Frequency (BMUF) of ionospheric F2-Layer has been made. A mid-latitude region selected for this research work by using data from station Wakkanai ($45.38^{o} N$, $141.66^{o} E$). This study included 12 monthly median data from year (2001, $R_{12}=111$) selected for high Sunspot number (SSN) and years for low SSN (2004, $R_{12}=44$) and (2005, $R_{12}=29$). Frequency parameters foF2 reveals that there is a good correlation between observed and predicted except for January of years 2001 and 2004, and BMUF revealed that there is a good correlation between observed and predicted for years of low SSN and all months except in month 1, 9 and 12 of year 2004, for year 2001 of high SSN there is a bad correlation. A correction factor as a function of time used from fitting technique to correct the predicted value with observed value of BMUF for year 2001.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

8 extracted references · 8 canonical work pages

[1]

INTRODUCTION The maximum usable frequency (MUF) is important ionospheric parameter for radio users because of its role in radio frequency management and for providing a good communication 2 link between two locations (Athieno et al., 2015; Suparta et al., 2018). MUF would be used to designate the highest signal frequency for high frequency (HF) communicat...

work page 2015
[2]

DATA SELECTION Ionosonde data station was used for comparison with IRI model, the station chosen was Wakkanai station (latitude 45.38oN, longitude 141.66oE) for calculating basic monthly 3 median MUF from observed data of the F2 layer critic al frequency (f0F2) and M3000F2 for selected years (2001, 2004 and 2005) . The degree of correlation between daily ...

work page 1998
[3]

DATA ANALYSES To study the BMUF we need to calculate the critical frequency (predicted) foF2 and M3000F2 from t he IRI model by using CCIR coefficient for years selected (2001) for high SSN and (2004, and 2005) for low SSN and compared with data observed. In figure 6 is a good correlation between observed BMUF and predicted for years (2004,2005) for SSN l...

work page 2001
[4]

In winter season foF2 values higher than summer season for high and low SSN this is anomaly in mid-latitude region

RESULTS AND DISCUSSION Figures (1 and 2) represent the observed and predicted monthly median foF2 with local time for three years 2001, 2004, and 2005 respectively, in which it reveal that the critical frequency have a high value in the day and low in the night. In winter season foF2 values higher than summer season for high and low SSN this is anomaly in...

work page 2001
[5]

Ionospheric data from the ionosonde stations such as Wakkanai station can be used to monitor this environment by observing Mid- latitude propagation conditions

SUMMARY Space weather effects can seriously impact HF communications by changing the ionospheric environment through which the radio waves propagate. Ionospheric data from the ionosonde stations such as Wakkanai station can be used to monitor this environment by observing Mid- latitude propagation conditions. From drawing f oF2 and BMUF with local time fo...

work page 2001
[6]

ACKNOWLEDGEMENTS The data are provided from WDC for Ionosphere, Tokyo, National Institute of Information and Communications Technology

work page
[7]

REFERENCES Adeniyi, J., Bilitza, D., Radicella, S., & Willoughby, A. (2003). Equatorial F2 -peak 5 parameters in the IRI model. Advances in Space Research, 31(3), 507-512. Athieno, R., Jayachandran, P., Themens, D., & Danskin, D. (2015). Comparison of observed and predicted MUF (3000) F2 in the polar cap region. Radio Science, 50(6), 509-517. Bahari, S. A...

work page 2003
[2013]

which fluctuate continuously because the ionosphere acts as a dispersive medium (Athieno et al., 2015). MUF is simply given by (Fotiadis et al., 2004; Oyekola, 2010; Malik et al., 2016): MUF = foF2 M(3000)F2, where foF2 is th e critical frequency of the F2 layer, i.e., the highest frequency that would be reflected by the ionosphere at vertical incidence (...

work page 2015

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

INTRODUCTION The maximum usable frequency (MUF) is important ionospheric parameter for radio users because of its role in radio frequency management and for providing a good communication 2 link between two locations (Athieno et al., 2015; Suparta et al., 2018). MUF would be used to designate the highest signal frequency for high frequency (HF) communicat...

work page 2015

[2] [2]

DATA SELECTION Ionosonde data station was used for comparison with IRI model, the station chosen was Wakkanai station (latitude 45.38oN, longitude 141.66oE) for calculating basic monthly 3 median MUF from observed data of the F2 layer critic al frequency (f0F2) and M3000F2 for selected years (2001, 2004 and 2005) . The degree of correlation between daily ...

work page 1998

[3] [3]

DATA ANALYSES To study the BMUF we need to calculate the critical frequency (predicted) foF2 and M3000F2 from t he IRI model by using CCIR coefficient for years selected (2001) for high SSN and (2004, and 2005) for low SSN and compared with data observed. In figure 6 is a good correlation between observed BMUF and predicted for years (2004,2005) for SSN l...

work page 2001

[4] [4]

In winter season foF2 values higher than summer season for high and low SSN this is anomaly in mid-latitude region

RESULTS AND DISCUSSION Figures (1 and 2) represent the observed and predicted monthly median foF2 with local time for three years 2001, 2004, and 2005 respectively, in which it reveal that the critical frequency have a high value in the day and low in the night. In winter season foF2 values higher than summer season for high and low SSN this is anomaly in...

work page 2001

[5] [5]

Ionospheric data from the ionosonde stations such as Wakkanai station can be used to monitor this environment by observing Mid- latitude propagation conditions

SUMMARY Space weather effects can seriously impact HF communications by changing the ionospheric environment through which the radio waves propagate. Ionospheric data from the ionosonde stations such as Wakkanai station can be used to monitor this environment by observing Mid- latitude propagation conditions. From drawing f oF2 and BMUF with local time fo...

work page 2001

[6] [6]

ACKNOWLEDGEMENTS The data are provided from WDC for Ionosphere, Tokyo, National Institute of Information and Communications Technology

work page

[7] [7]

REFERENCES Adeniyi, J., Bilitza, D., Radicella, S., & Willoughby, A. (2003). Equatorial F2 -peak 5 parameters in the IRI model. Advances in Space Research, 31(3), 507-512. Athieno, R., Jayachandran, P., Themens, D., & Danskin, D. (2015). Comparison of observed and predicted MUF (3000) F2 in the polar cap region. Radio Science, 50(6), 509-517. Bahari, S. A...

work page 2003

[8] [2013]

which fluctuate continuously because the ionosphere acts as a dispersive medium (Athieno et al., 2015). MUF is simply given by (Fotiadis et al., 2004; Oyekola, 2010; Malik et al., 2016): MUF = foF2 M(3000)F2, where foF2 is th e critical frequency of the F2 layer, i.e., the highest frequency that would be reflected by the ionosphere at vertical incidence (...

work page 2015