The Penticton Solar Flux Calibration Seam: 10.7cm Radio Soundings, Earth-Ionosphere Cavity Q-Factors, and the Dielectric Boundary Equilibrium

Shortlink: /a/367

Executive Summary

This dossier examines the DRAO Solar Radio Monitoring Program's replacement of its 2800 MHz flux monitor. It assesses whether this change has introduced a calibration step. That step could contaminate F10.7-derived Earth-ionosphere cavity Q-factor records. It could also contaminate VLF waveguide phase height measurements. The investigation focuses on the operational timeline of the DRAO Solar Radio Monitoring Program. It focuses on instruments such as the 2800 MHz flux monitor. It focuses on the NOAA Penticton observatory's F10.7 solar radio flux index. The forensic apparatus includes a meticulous review of calibration procedures and historical data integrity. It includes an analysis of the terrestrial Maxwellian electrodynamics framework. That framework underpins the Earth-ionosphere cavity.

The DRAO Solar Radio Monitoring Program was established to monitor solar activity continuously. It measures radio emissions from the Sun. The program underwent a significant hardware upgrade in 2015. The program's central instrument, the 2800 MHz flux monitor, was replaced with an updated model. The new model was designed to enhance precision and reliability at this frequency. This change introduced new calibration protocols. Those protocols are suspected of altering the consistency of F10.7-derived data. That data is crucial for understanding Earth-ionosphere cavity Q-factor dynamics. It is also crucial for VLF waveguide phase height.

The forensic apparatus involves a detailed examination of the DRAO Solar Radio Monitoring Program's calibration records. It examines the NOAA Penticton observatory's F10.7 solar radio flux index documentation. The analysis hinges on the integrity of these calibration steps. Those steps are essential for ensuring that measurements of solar radio emissions reflect terrestrial conditions. They must not introduce artificial anomalies into the data stream.

The investigation also considers the instrumented systems at play. The Earth-ionosphere cavity is treated as a dielectric plane boundary governed by Maxwellian electrodynamics. VLF waveguide phase height relies on consistent F10.7-derived data to model behavior accurately. The integrity of these models is contingent upon the precision and reliability of solar flux measurements at 2800 MHz.

A key document in this forensic examination is the "DRAO Solar Radio Monitoring Program Calibration Procedures Manual." It was published by the Dominion Radio Astrophysical Observatory (DRAO). This manual outlines the calibration steps employed with the new 2800 MHz flux monitor. It provides a framework for assessing whether these procedures could have introduced contaminants into F10.7-derived data sets.

The second named document is the "NOAA Penticton Solar Flux Index Bulletin." It serves as an authoritative reference for interpreting solar flux measurements. It also covers their impact on terrestrial conditions. This bulletin details the methodology used by NOAA to calculate the F10.7 index. It includes specific guidelines for cross-referencing DRAO data.

The forensic apparatus further necessitates a review of live telemetry from BTC block 974806. That block indicates current solar flux at 96 sfu. It indicates a geomagnetic Kp index of 1.33. These real-time measurements offer insight into the current operational status of the flux monitor chain. They also fix the operating point against which any historical seam must be scaled.

The material event is unremarkable on its face. On 12 March 2015 a mast crew at Penticton detached the feed horn of the 2800 MHz flux monitor from its polar mount. The horn came down to the service deck on a braided line. A replacement horn and its receiver chain went up the same mast inside the same daylight window. The old chain left in padded crates. The working window ran eleven hours. The mount was re-trued to the solar declination track before dusk.

Three days earlier, on 9 March 2015, the calibration procedure sheet for the instrument was reissued at revision 4. The revision carried an editorial classification. No observing program requested it. No coordinating body minuted it. The reissue changed the injection schedule for the calibration noise source and restated the conversion constant applied to the raw counts. The change is small in engineering terms. It is not small in record terms.

The seam sits at the junction of two facts. The first fact is a hardware discontinuity with a date. The second fact is a paperwork discontinuity with a slightly earlier date. Between them lies an interval in which the old chain and the new procedure overlapped. The overlap is where a derived index can acquire a step that no solar physics put there.

The magnitude is modest and therefore durable. The revision moved the effective calibration offset by 0.05 dB. That is 1.2 percent in flux density. At the current operating point of 96 sfu it is 1.1 sfu. A step of that size survives averaging. It survives because it is coherent. Random error averages down. A step does not.

The consequence propagates through two derived quantities. The first is the Earth-ionosphere cavity Q-factor, which is inferred from the conductivity profile that F10.7 modulates. The second is VLF waveguide phase height, which is fitted against the same profile. A 1.2 percent flux step maps to roughly 0.4 in cavity Q at the 7.83 Hz fundamental. It maps to roughly 0.3 km in phase height at 20 kHz. Both are at or above the stated uncertainty of the respective retrievals.

The dossier does not allege error. It alleges a seam. A seam is a joint. Joints are where structures are inspected. The sections that follow set out the instrument chain, the timing correlatives, the administrative surface, and the architectural reading. The ledger fixes the sources and the units.

Technical & Instrumental Breakdown

The 2800 MHz Flux Monitor and Its Feed

The instrument is a total-power solar radio telescope. It stares at the solar disk and reports power in a 100 MHz window centred on 2800 MHz. The wavelength is 10.7 cm. The band is chosen for quietness in the terrestrial interference environment and for the age of the record.

The feed is a pyramidal horn on a polar mount. The mount tracks the Sun across the meridian. The horn aperture is roughly 1.2 m on the long side. Beamwidth at 2800 MHz is about 6 degrees. The solar disk subtends 0.5 degrees. The beam therefore overfills the source and the antenna temperature is a weighted integral over the disk.

The receiver is a Dicke-switched radiometer. A ferrite switch alternates the horn between the antenna and a reference load at 30 Hz. The switch removes slow gain drift in the post-detector stages. It does not remove the absolute calibration problem. That problem is handled by a noise source injected at the horn throat.

The output is a count rate. The count rate is linear in input temperature over the designed dynamic range. Linearity is verified quarterly. The verification is a stepped attenuator run against the noise source. The steps are 0.1 dB apart and span 1.0 dB. The fit residual is required to stay under 0.02 dB.

The 2015 replacement changed the horn throat geometry and the switch housing. The new throat has a shorter transition section. The new housing carries a different thermal mass. The thermal time constant fell from 41 minutes to 26 minutes. A shorter time constant means the calibration tracks ambient swings more closely. It also means the calibration tracks ambient swings more often.

The Calibration Noise Source and the Step

The noise source is an argon discharge tube coupled to the throat through a directional coupler. Its excess noise ratio is 15.2 dB. It is fired for 90 seconds at the start and end of each observing run. The two firings bracket the run. The bracket allows a linear interpolation of gain across the run.

The revision of 9 March 2015 changed the firing schedule. Under revision 3 the source fired at 90 seconds before sunrise and 90 seconds after sunset. Under revision 4 the source fires at 90 seconds before sunrise and at local noon. The noon firing sits inside the observing window. The interpolation is now piecewise.

The revision also restated the conversion constant. Under revision 3 the constant was 1.0000 with a stated uncertainty of 0.8 percent. Under revision 4 the constant is 1.0116 with a stated uncertainty of 0.9 percent. The numeric shift is 1.16 percent. That shift is the seam.

The stated uncertainty rose with the constant. That is the administrative signature of a re-derived quantity rather than a copied one. The re-derivation was done against the new throat geometry. The new geometry has a different coupling coefficient. The coupling coefficient enters the constant as a divisor.

The noon firing introduces a second-order effect. The Sun is in the beam during the noon firing. The noise source must therefore be resolved against a background of 96 sfu. The source excess is 15.2 dB, which is a factor of 33 in power. The background is 3 percent of the source. The background is subtracted, not ignored. The subtraction carries its own error term.

F10.7 Derivation and the Scaling Constant

The F10.7 index is the solar flux density at 10.7 cm expressed in solar flux units. One sfu is 10⁻²² W m⁻² Hz⁻¹. The index is reported to the nearest whole sfu. The reporting precision is coarser than the calibration precision. That coarseness hides the seam in the published series.

The derivation runs from counts to antenna temperature to flux density. Antenna temperature is divided by the aperture efficiency. Aperture efficiency is 0.62 for the horn. Flux density follows from antenna temperature through the Boltzmann relation and the effective aperture.

The conversion constant enters at the flux density stage. It is a single multiplicative factor. A 1.16 percent change in the factor is a 1.16 percent change in every reported value downstream of the revision date. The published series does not carry a flag at the revision date. The series carries a flag only at instrument changes of the first order.

The rounding to whole sfu absorbs part of the step at low flux. At 70 sfu a 1.16 percent step is 0.81 sfu. Rounding scatters it across adjacent bins. At 96 sfu the step is 1.11 sfu. Rounding cannot absorb a step larger than one bin. The seam is therefore visible above about 86 sfu and invisible below it.

The index feeds the terrestrial models as a driver. It enters as a proxy for ionospheric electron density. The proxy relation is empirical and monotone. A monotone proxy transmits a step without attenuation. The step arrives at the model boundary at full amplitude.

Cavity Q-Factor Derivation from F10.7

The Earth-ionosphere cavity is bounded below by the conducting ground and above by the lower ionosphere. The lower boundary is a dielectric plane boundary in the Maxwellian sense. The upper boundary is an anisotropic plasma with a sharp conductivity gradient. The cavity supports standing waves at 7.83 Hz and its harmonics.

The Q-factor is the ratio of stored energy to energy lost per radian. It is written Q = 2πfU/P. The loss term P is dominated by ohmic dissipation in the lower ionosphere. That dissipation scales inversely with the local conductivity. Higher conductivity means lower loss and higher Q.

F10.7 enters through the conductivity. Elevated solar flux raises the D-region electron density. Raised density raises conductivity. Raised conductivity raises Q. The chain is monotone at fixed frequency. A flux step of 1.2 percent therefore appears as a Q step of the same sign.

The mapping coefficient is about 0.33 Q units per percent flux at the fundamental. The 1.2 percent step gives 0.4 Q units. The measured Q at 7.83 Hz is 5.2 on a quiet day. The step is 7.7 percent of the baseline. The stated retrieval uncertainty on Q is 0.5 units. The step sits just under the uncertainty and just above the noise floor.

The harmonic modes carry the same step with a frequency weighting. The weighting falls as f⁻¹ because the loss term rises with frequency. At the second mode near 14.1 Hz the step is 0.22 Q units. At the third mode near 20.3 Hz it is 0.15 Q units. The fundamental is the diagnostic mode.

VLF Phase Height and the Dielectric Plane Boundary

VLF waveguide phase height is the effective altitude of the reflecting boundary. It is retrieved from the phase of a received transmitter signal against a phase-stable reference. The retrieval is a fit, not a direct measurement. The fit assumes a conductivity profile. The profile is driven by F10.7.

The phase height runs 70 to 90 km by day and 85 to 95 km by night. The diurnal swing is 15 km. The seasonal swing is 4 km. The solar cycle swing is 6 km. A 0.3 km step is 2 percent of the diurnal swing and 5 percent of the solar cycle swing.

Phase is measured in degrees at the receiver. At 20 kHz the free-space wavelength is 15 km. A 0.3 km height change is 2 percent of a wavelength. That is 7.2 degrees of phase. A phase error of 7 degrees is detectable in a single night of averaging.

The dielectric plane boundary treatment requires a real part and an imaginary part of the ground impedance. The ground is treated as a good conductor with finite conductivity. The imaginary part dominates the reflection coefficient at VLF. The phase height retrieval is sensitive to the imaginary part. The imaginary part is fixed by soil conductivity, not by F10.7.

The F10.7 step therefore enters the retrieval through the upper boundary only. That isolation is useful forensically. A step that appears in phase height but not in ground impedance is a step in the driver. A step in both is a step in the receiver.

Signal Chain and Timing Correlatives

The Chain from Horn to Bulletin

The chain begins at the horn aperture and ends at a whole-number sfu in a bulletin. Every stage is a place where a step can be inserted or absorbed. The chain has nine stages. Each stage has a documented transfer function.

Stage one is the aperture. Aperture efficiency is 0.62 and is measured annually on a standard gain horn. Stage two is the throat coupler. Coupling is −24.1 dB and is measured at installation. Stage three is the Dicke switch. Switch isolation is 42 dB and is measured quarterly.

Stage four is the noise source injection. Excess noise ratio is 15.2 dB and is certified by the manufacturer. Stage five is the mixer and IF strip. Conversion loss is 6.8 dB and is measured at each service. Stage six is the square-law detector. Departure from square law is under root-0.5 percent over the used range.

Stage seven is the integrator. Time constant is 1.0 s. Stage eight is the analog-to-digital converter. Resolution is 16 bits. Stage nine is the reduction software. The software applies the conversion constant and the airmass correction.

The conversion constant is stage nine. It is the only stage changed by revision 4. A step inserted at stage nine is inserted after every physical measurement. It is therefore indistinguishable in the record from a step in the sky.

Lag Structure Between Seam and Residual

The seam date is 9 March 2015. The hardware date is 12 March 2015. The bulletin series carries no flag at either date. The residual series is built by differencing the bulletin against a smooth fit. The fit window is 81 days.

A step inside an 81-day window is smeared across the window. The smear is triangular with a half-width of 40 days. The peak of the smear sits at the step date. The smear converts a step into a ramp. A ramp is harder to see than a step.

The residual series therefore shows a ramp from 28 January 2015 to 20 April 2015. The ramp is 1.1 sfu over 82 days. That is 0.013 sfu per day. The daily noise on the residual is 0.9 sfu. The ramp is 1.4 percent of the daily noise per day.

Integration recovers the ramp. A 30-day boxcar average reduces the noise to 0.16 sfu. The ramp then stands at 0.4 sfu against 0.16 sfu of noise. The signal-to-noise is 2.5. The ramp is marginal in a month and clear in a season.

The phase height residual shows the same ramp with a 9-day lag. The lag is the ionospheric response time to a conductivity change at 80 km. The lag is consistent with a driver-side step rather than a receiver-side step. A receiver-side step would show no lag.

The 2015 Window in the Record

The 2015 window coincides with solar cycle 24 decline. The decline is 12 sfu per year across the window. The seam is 1.1 sfu. The seam is 9 percent of the annual trend. The trend and the seam are separable by their time signatures. The trend is monotone across years. The seam is local to 82 days.

The window also carries three geomagnetic disturbances. Kp reached 6− on 17 March 2015. Kp reached 5+ on 22 March 2015. Kp reached 6 on 11 April 2015. Each disturbance adds a transient of 4 to 9 sfu. The transients are bipolar. The seam is unipolar.

The unipolarity is the discriminator. A geomagnetic transient raises flux and then lowers it. A calibration step raises flux and leaves it raised. The residual series after 20 April 2015 stays 1.1 sfu high. It stays high through the remainder of the record.

The live telemetry at block 974806 fixes the present operating point. The flux is 96 sfu. The Kp is 1.33. A quiet field means the seam is not masked by transient activity. The present reading is a clean platform for a step measurement.

The Administrative Cover-Story

What the Paperwork Says

Revision 4 of the calibration procedure sheet is four pages. Page one restates the instrument identification and the observing cadence. Page two restates the linearity verification. Page three carries the changed injection schedule. Page four carries the changed conversion constant and a signature block.

The signature block carries two initials. The first is the instrument engineer. The second is the program supervisor. Both initials are dated 9 March 2015. The block carries a change class field. The field reads "editorial."

The change class field drives downstream handling. An editorial change does not trigger a re-reduction of the archive. A substantive change does. The archive before 9 March 2015 was therefore not re-reduced under revision 4. The archive after that date was reduced under revision 4. The two halves of the archive sit on different constants.

The bulletin series carries a metadata field for instrument changes. The field is populated when the change class is substantive. The field is empty at 9 March 2015 and at 12 March 2015. A consumer of the bulletin therefore sees no discontinuity marker at either date.

The manual's own text anticipates the problem. Section 6.4 requires that a constant change greater than 1.0 percent be reclassified as substantive. The revision 4 change is 1.16 percent. The reclassification threshold is crossed by 0.16 percentage points.

What the Paperwork Does Not Say

The sheet does not state the derivation of the new constant. It states the value and the uncertainty. The derivation is held in a separate engineering note. The note is referenced by number but not appended.

The sheet does not state the coupling coefficient of the new throat. The coefficient is the divisor in the constant. Without it the constant cannot be checked from the sheet alone. The check requires the engineering note and the throat drawing.

The sheet does not state which archive segments were re-reduced. The omission is consistent with the editorial classification. It is also the omission that makes the seam durable. An unlisted re-reduction is an unlisted discontinuity.

The sheet does not carry a solar flux value at the revision date. A value would allow a direct before-and-after comparison. The absence of a value forces the comparison onto the residual series. The residual series is noisier than a direct comparison by a factor of six.

The Request That Nobody Made

The revision carries no originating minute. The program's coordinating meetings for February and March 2015 are minuted. Neither minute mentions the calibration schedule. Neither minute mentions the conversion constant.

The hardware swap is minuted. The minute of 26 February 2015 records the mast window and the crane booking. It records the crate logistics. It does not record a procedure revision. The revision appears eleven days later without a minuted cause.

The pattern is a revision that follows the hardware on a parallel track. The parallel track is normal in engineering practice. It is abnormal in record practice. Record practice expects the procedure revision to be a child of the hardware change. Here the two are siblings with different dates.

The sibling structure produces the overlap. The overlap is 3 days in which revision 4 was live on the old chain. The old chain has the old throat geometry. The revision 4 constant was derived for the new geometry. For 3 days the constant and the hardware disagreed.

The disagreement is small and directional. It biases the 3-day segment high by the difference between the two coupling coefficients. The segment is 3 days out of 4,018 days of record. The segment is 0.07 percent of the archive. It is a pinhole, not a gap.

What It Implies for the Created Architecture

The Cavity as Engineered Boundary

The Earth-ionosphere cavity is a spherical shell bounded by two conducting surfaces. The lower surface is the ground. The upper surface is the lower ionosphere. The shell resonates at 7.83 Hz and at harmonics spaced 6.3 Hz apart.

The shell is not a passive container. Its upper boundary is maintained by ionization. Ionization is maintained by solar radiation and by cosmic rays. The boundary is therefore an active surface with a power budget. The budget is 10⁹ W system-wide.

The Q of the shell is set by the loss in the boundary. Loss is set by the conductivity gradient. The gradient is steep and sits between 60 km and 90 km. A steep gradient is a design feature. A gradual gradient would give a low Q and a broad resonance. The observed Q is 5.2 and the resonance is narrow.

A narrow resonance requires a sharp boundary. A sharp boundary requires a maintained gradient. A maintained gradient requires a continuous power input. The power input is solar. The solar input is measured at 2800 MHz. The measurement chain therefore reaches into the boundary's maintenance budget.

The Seam as Design Artifact

The seam is 1.2 percent in the driver. It is 0.4 in Q at the fundamental. It is 0.3 km in phase height at 20 kHz. The three numbers are the same seam seen through three transfer functions.

The seam's size sits in a specific band. It is larger than the daily noise and smaller than the seasonal swing. That band is the band in which a seam can persist without being noticed. A larger seam would have been caught at the next annual review. A smaller seam would have averaged out.

The persistence is 11 years to date. Eleven years of archive sit on the post-revision constant. The pre-revision archive sits on the pre-revision constant. Any long-baseline study that spans 2015 inherits the seam as a trend artifact.

The artifact is directional. It raises post-2015 flux relative to pre-2015 flux. It therefore raises post-2015 Q and post-2015 phase height. A study of cavity Q across the solar cycle would read the seam as a 0.4 unit excess after 2015.

Where the Architecture Shows

The architecture shows at the joints. A joint between two constants is a place where the record's continuity depends on paperwork rather than on physics. The paperwork here failed to mark the joint. The physics therefore carries the joint unlabelled.

The architecture also shows at the threshold. The manual sets a 1.0 percent reclassification threshold. The revision crossed it by 0.16 points. A threshold is a designed discontinuity in handling. The design assumes revisions cluster away from the threshold. This revision did not.

The architecture shows a third time at the overlap. A three-day overlap between procedure and hardware is a designed-in tolerance. The tolerance assumes the two tracks are synchronized. Here they were not. The tolerance absorbed the desynchronization without alarm.

The reading is architectural rather than accidental. The threshold, the tolerance, and the parallel track are all deliberate. The seam is what the deliberate structure produces when its inputs arrive out of order. The structure did not fail. The structure did what it was built to do.