by Joe Cerniglia
Lately I have been taking a new look at the TIGHAR Radio Signal Catalog. It is a masterpiece of forensic detail that, as a veteran data scientist, I can truly appreciate. Most worthy of consideration is Bob Brandenburg's landmark article called Time and Tide. Bob was the first person to understand that an accurate tidal hindcast of Nikumaroro could yield new insights into the relationship between the height of the water on the reef flat, the time of day, and the ability of the Lockheed Model 10E to transmit distress calls.
What Bob's graphical analysis did not attempt, however, was to unify the entire post-loss dataset into a single continuous view, complete with the day-night cycles, the height of the tides, and the catalog of all reported signals from Earhart. Instead, Bob showed 24-hour snapshots, small multiples of sets of radio messages graphed against the tidal patterns. Additionally, Bob limited his analysis only to the signals judged to be credible by TIGHAR. The non-credible and uncertain signals are a source of information as well, tenuous as they might be.
A new graph I have constructed of the timeline of radio signals reaffirms that the sun's ionization of the atmospheric D-Layer[1] during daytime on Nikumaroro prevented listeners from hearing Amelia Earhart's and Capt. Fred Noonan's distress calls, even though credible evidence exists these calls were made.
In 2013, when the Time and Tide analysis was constructed, drawing professional-grade charts was a far more laborious process whose finished product, for all but those with access to the best platforms, hardware, and private software, was far from what one could envision. MATLAB and Adobe Illustrator were state-of-the-art tools, offering more sophisticated charting capabilities than the usual Excel and PowerPoint. Computers could easily crunch the numbers, but the weakest link was the output. Today, AI can easily ingest the data and create a Python program (and programs in many other languages) to actualize any design concept the user wants to implement. The process is far from instantaneous, and vetting and checking one's work is no less rigorous a process than it was back in 2013. This graph was built over the course of three solid days of effort, a stepwise refinement, a virtual conversation with AI, that required an advanced knowledge of Python and the Matplotlib library, which I have, as well as years of personal research of the radio signals themselves. The work still requires concentration and experience, but the tools have advanced to meet the level of one's own ideas. Graphing becomes an extension of the mind rather than a laborious translation process with finicky tools and complex programming languages, which, even in the hands of an expert, can be extremely tricky.
Here is a new compendium graphical analysis of radio catalog signals from July 2 - 9, 1937:
Note: This forensic timeline contains fine details; pinch-zooming will aid in seeing these details more clearly.
The Electra 10E, symbolized by a red airplane in the graph, must land no later than hour 10.9868 (10:59 am Nikumaroro time) with a tidal height of exactly 0.4967 feet (5.78 inches) to remain within the recommended cutoff for a safe landing (6 inches).[3] This allows a reasonable buffer of time to reach Nikumaroro after Earhart's message received by Itasca ("We are on the line...") at 8:43 am (9:13 am Nikumaroro time).
Zero feet on the vertical axis is the physical location where the tires of the airplane met the ground when it pulled to a stop, prior to taxiing. Because I am already accounting for the reef's average mean base height of 1.8 feet in my tidal calculations, zero is the datum point. I allow the Electra 10E to taxi to a ground position six (6) inches higher than the landing point, an exigency measure any reasonable pilot would take to protect the airframe. This gains a 6-inch vertical safety buffer, meaning the incoming tide must rise an additional six inches (0.5 feet) before it can breach any of three critical constraint boundaries on the mechanical operation of the radio and of the airplane. These constraints, represented as horizontal lines, are:
1. Lower constraint: Optimal Engine Charging Zone. Water Depth <= 1.5 ft. → 1 foot of operational clearance + 0.5 feet of taxi elevation.This boundary existed because the reef on Nikumaroro is an extremely dynamic water environment. Currents and swells can easily exceed the tidal depth at given moments. The only way to ensure the propellers are clear and stay clear of the water so that they can spin and charge the battery is to run them when the tide is this low.[4]
2. Middle constraint: Propeller Clearance Limit and Generator Cutoff. Water Depth = 2.66 feet. → 2.16 feet of operational clearance + 0.5 feet of taxi elevation.
This is the absolute limit of the height of the water at which the propellers can spin and charge the battery for brief periods, but the winds would need to be very low and the waves calm to charge as the water approached this limit.[5]
3. Upper constraint: Transmitter Submersion Ceiling and Terminal Short Circuit Threshold. Water Depth = 3.45 feet. → 2.95 feet of operational clearance + 0.5 feet of taxi elevation.This is the limit at which the airplane can keep the transmitter out of the water. Once this limit is exceeded, a catastrophic short circuit instantly discharges the entire electrical grid into the ocean, resulting in permanent system failure and making any further transmission an absolute physical impossibility.[6]
The heights that the water had to exceed are accurate for each constraint, given that we know the heights of various locations on the airplane. Even so, there is no way for anyone to know the precise height of the water relative to a parked airplane on Nikumaroro at a given moment in 1937. The reef on Nikumaroro is not a flat plain, nor is the water a calm swimming pool. However, the exact measurements for the specific conditions are not as important as illustrating that the constraints were present and to illustrate the effect they had on winnowing received signals, and on winnowing transmitted signals.
The graph does well in showing the rising frequency and urgency of transmissions only to show them tapering off toward the later dates as equipment began to fail. Restraint and by-the-book calm in the evening hours of July 2, when the tide was in the safe clearance zone to turn the propeller, gave way to an apparently greater urgency during the later days, when riskier transmissions were tried at higher water levels. (See July 2, 3, and 4 for that trend.)
Note also that the daytime periods on Nikumaroro have scant received transmissions, but there are a few notable exceptions from casual listeners (Nina Paxton on July 3, Betty Klenck on July 5, and Thelma Lovelace on July 6). This seems to indicate not that Earhart and Noonan gave up trying during the day, but rather that only harmonic multiples of their frequency could be picked up during daylight, bouncing off the ionosphere to land thousands of miles away on the continental United States.
What is also interesting is that the radio catalog's methodology for assessing credibility infrequently mentions tides. (Brandenburg's idea to measure the tides had not even been conceived of when the catalog was compiled.) They were not the primary factor in ruling on the credibility of the various signals; therefore, the vertical axis of the graph, which shows winnowing based on water levels, functions as a kind of independent auditor of the overall credibility of the catalog.
The signals cluster on the graph where the tide is low AND the time is night. When the tide is high and it is nighttime, the signals drop in number, although they are still heard in a great number in the early morning of July 4 at a rising and high tide, with seven signals over the course of five days (July 2, 3, 4, 5, and 8) clustering like bees, a dual-axis convergence, at the absolute and precise apex of high tide.[7] When the tide is low and it is daytime, the signals attenuate almost to nothing. Many of the nights had both high and low tide. (This is why Pacific tides are called semi-diurnal.) The best nights for transmission were the late evening of July 2 and the late evening of July 3. After the early morning hours of July 5, the number of transmissions decreases significantly.
The tides, for all of their severity and relentless march and retreat across the graph, were a less severe taskmaster than the day-night boundaries. Those were very nearly absolute, save for a few scattered daytime receptions by astute listeners with very capable radios in the mainland United States. If the tides remained below the critical 3.45-foot transmitter submersion ceiling, they could only dictate, at their best, the ability to transmit by strangling the propeller system and enforcing a transmission regimen on highly finite battery reserves only. They could also, no doubt, have made working inside the airplane very tense and uncomfortable. All of this winnowed the signals, but it did not stop them. The day-night boundaries, by contrast, strongly dictated the probability that any one transmission could be received at all.
These day-night boundaries plotted on the graph are highly accurate, mirroring to the minute the exact astronomical times of sunrise and sunset experienced on Nikumaroro in July 1937.[8] AI provides the following tolerances for the computed tide model:
Tidal height: ±6 to 12 inches, to account for the transient, real-time meteorological noise on the ground.
Tidal minima and maxima: ±15 minutes
Frequency of minima and maxima: ±0
To generate the waveforms on the graph, I used two custom Python scripts to calculate a localized hydrodynamic tidal model.
With the assistance of AI, I wrote these two Python programs. The first is a script that combines the gravitational pull of the moon and the sun, matching the exact cycle speeds of five different ocean waves (the five basic tidal constituents).
While the angular velocities of all five astronomical constituents are fixed and invariant, the geomorphic phase lag array for these constituents functions as a highly optimized environmental reconstruction of the local reef flat.[9] Rather than reflecting a sterile, deep-ocean baseline, these parameters programmatically capture the significant shallow-water dynamics and reef-friction lags native to Nutiran on Nikumaroro. For more on how the computational engine arrived at the empirical convergence lock for the geomorphic phase lag array, see note 9 below.
The mathematical ratio between these waves naturally replicates the exact oceanographic physics of the Phoenix Island group. The program combines these waves chronologically, programmatically capturing how tidal ranges naturally expand or contract based on the shifting astronomical alignments of the moon and the sun. A corrective function to account for the neap-to-spring tide transition, which happened during the first week of July 1937, is also included in the tide calculator.[10] The program saves the results into a data file called nikumaroro_projected_tides.csv.
The second script, the main charting program, opens up that fresh data file and uses linear interpolation to fill in any gaps between the exact hours. This allows the program to automatically look up any radio signal's exact timestamp, figure out precisely how deep the water was at that exact minute, and plot all of the received signal times directly onto the timeline's wave curves. Weather and wind at those exact times will have played a role in changing the currents and tides. Although I do not know exactly where an airplane would have parked near the SS Norwich City, this geodetic reconstruction is a good one in that it creates a realistic portrayal of the natural variability and push and pull of tides over the period of one week.
The graph also includes the Lambrecht overflight, shown on the right side of the graph by a tiny airplane with a red cross. The calculated height of the tides at the time Lambrecht flew over Nikumaroro, approximately 9:15 am on July 9, 1937, is included in the file named nikumaroro_projected_tides.csv in lines 179 and 180 . The calculation states the tide was between 2.92 and 2.99 feet high. This measurement correlates very well with the Lambrecht photo of Nikumaroro taken from the airplane as it flew overhead, which appears to show something like a high tide.
The Lambrecht photo, and the tidal data that the Python program furnishes to accompany the time the photo was taken, serve as a very important corroborative check on the accuracy of the waveforms in this analysis. While not anything like a measurement to professional hydrographic standards, this photo confirms that the approximate time that one of two high tides occurred on June 9, 1937 corresponds very well with the tidal data in the file. One may see on the graph that high tide occurred a few minutes after the Lambrecht flight and that an even higher high tide occurred at 9 pm that evening.
The gold, curved line on the graph illustrates the correspondence between the matching latitude and longitude that Ray Havens[11] (July 7) and Nina Paxton[12] (July 3) both gave in their accounts of receptions they stated were from Amelia Earhart. Since Ms. Paxton's account, which omitted compass headings, only came to public attention in the 1960s, there was no way for Mr. Havens to have copied his coordinates from Paxton. Paxton, however, might have copied from Havens since her typescript mentions August 10, and so had to have been written after Haven's coordinates were in the national press. Perhaps, alternatively, there was an independent third-party source for this information and the source for it was the post-loss radio signals.
Havens' account is on the left and Paxton's private typescript is on the right.
173°W, 5°S is 107 miles ESE of Nikumaroro.
In the interest of reproducibility of research, a concern I highlighted in my earlier paper in March of 2022, Machine Learning with Amelia, I am attaching the Python programs and data files that created this graph:
- Tide generator for Nikumaroro.py
- nikumaroro-fixed-layout_final.py
- University of Hawaii Sea Level Center Station 013 (Kanton) hourly historical records (1972-2026) Note that this file is large (475,536 rows), so it may take a few seconds longer than usual to download. If you would rather download the data from the original source, click here, find the row that has a UH# of 13 and choose the hourly csv.
- kanton_uhslc_harmonic_solver_commented.py
The first two programs are the core Python scripts. You will need to download and run these from the same directory to have the scripts coordinate properly with each other. Run the tide generator script first. You will be prompted to enter your landing date. Enter "1937-07-02" (no quotation marks) or simply hit Enter. This will generate your tides csv, which contains all the tidal data you need for the graph.[13] Next run the fixed-layout script. This will produce two output files. You will need to change the lines at the very end of the program to match your directory structure. This will direct the script as to where to put your graphical output.
The last two files are for your use if you are interested in verifying how the amplitude array was derived. The historical records file is the proxy record of hourly tidal heights over a 54-year period for Kanton Island.[14] You will need to modify the Python solver script in line 36 to represent where you stored the tidal history file when you downloaded it.
The solver script calculates amplitudes for Kanton, a basic deep-water calculation using ordinary least-squares matrix regression, and adjusts them for the localized dynamics of the reef environment of Nikumaroro. To do this adjustment, it uses what is known as Courtier's 0.50 Form Ratio.[15]
Courtier's 0.50 Form Ratio provides an honest, mathematical guarantee that the shape of the waveforms matches real-world human experience on the reef, rather than a sterile computer guess. On paper, the unadjusted open-ocean database constants project two nearly equal tides a day. But in practice, the wide, shallow coral shelf acts like a heavy hydraulic brake and a physical dam. It restricts drainage at low tide, with the resulting retained water blocking ingress at high tide, vertically damping the wave shape, and shifting the tide into a pattern dominated by severe diurnal inequalities. By locking this 0.50 ratio into the script, the model uses 54 years of real tidal records to ensure the natural damping and water-pooling caused by the submerged coral platform are accurately reflected across all 192 hours of the timeline. See the comments in the code for more details on this novel usage of Courtier's equation.
Also included is a pdf combining the radio receptions and the tidal heights at the time of each reception. An accompanying csv is also included (PDF | CSV).
Last, here is the Python script that produces the pdf and the csv.
Many have inquired with regard to how the heights of my tidal waveforms, hereafter referred to as the ECRAO analysis[16], compare with those of Bob Brandenburg's 2013 analysis, hereafter referred to as the legacy analysis.[17] This seemed a discussion worth exploring, if only to answer the question of why the ECRAO analysis should prove useful and very worthwhile in 2026.
Because the unattenuated 2013 EasyTide data for Hull Island that the legacy analysis used is no longer publicly reproducible from the UKHO service, exact row-for-row matrix comparisons are difficult. Nevertheless, the systemic structural differences are easily deduced in these main points.
A fair comparison requires selecting a unified zero baseline.[18] By establishing its chart datum relative to a reef section 0.43 meters (1 foot and 4.93 inches) higher than reference Point A, the legacy analysis projects the baseline wave curve downward relative to the landed aircraft. Mathematically, this acts as a direct vertical offset to compensate for the higher elevation parameter given to the Electra 10E. At the same time, the water-level constraints were left unchanged. This means that any comparison between waveforms in the ECRAO analysis, which did raise the constraints by 6 inches, and the legacy's, may reasonably add the amount of the 0.43-meter rise to the legacy's waveforms for the sake of equivalence. This equivalence also requires that the constraints remain at their revised heights that have been adjusted by +6 inches. In other words, a fair comparison requires that a single datum zero point be selected, and that datum is logically the point at which the tires of the Electra 10E met the reef flat when it came to a stop after landing, but before it taxied to a higher elevation. The higher elevation to which it taxied is purely accounted for in the ECRAO analysis by an upward adjustment of the three water-level constraints for the aircraft (listed above).
Even though it may be conceded that an elevation of 1 foot and 4.93 inches above the zero point on the graph probably exists somewhere on the Nutiran reef flat, its existence is no guarantee that the Electra could navigate to this specific spot on its own power. The required parking spot in the legacy analysis was arrived at through intensive surveying instrumentation, a luxury that Earhart and Noonan would not have had as they looked through their cockpit window trying to secure a survival footing on a foreign reef. By contrast, a six-inch elevation seems a much more readily achievable gain, comprising a taxiing distance of perhaps only a few feet shoreward. The legacy model's paper explicitly notes that while the 50-meter-wide landing strip was smooth, the reef flat immediately shoreward was "found too rough for landing, but suitable for taxiing."[19] For an exhausted crew rolling out a heavily fatigued aircraft, navigating to an area "50-meters shoreward of the landing area,"[20] slightly more than half the length of a football field, over an unsurveyed, fractured coral pavement presents a high operational hazard compared with a short, immediate shoreward adjustment.
Once a unified chart datum is established for both analyses, one may then analyze where the actual methodologies diverge. The baseline data that the legacy analysis used from Hull island was derived by the UKHO from primary ports using open-water constants.[21] Consequently, it completely lacked localized shallow-water attenuation factors like Courtier's 0.50 Form Ratio and failed to capture the non-linear pooling dynamics of the neap-to-spring tide transition. Because the legacy analysis applied a uniform linear regression formula
Tc = 1.156Th - 0.3998m
to bridge the islands, its mathematical engine simply carried these deep-water assumptions directly over to the Nikumaroro datum. The absence of shallow-water constraints in the legacy analysis means that it is possible to build a reasonable, shape-matched simulation of this unadjusted open-ocean methodology for the sake of comparison. By engineering a custom facsimile array that strips away localized coastal mechanics, this graph provides a highly effective control curve to contrast the legacy model's flatter baseline against the localized, fluid-forcing dynamics of the ECRAO model.
Figure 2.0: Demonstrating the Differences in Tidal Heights Between the Legacy Model and the ECRAO Model
This simulated open-ocean curve (dashed line) can accurately replicate the broader, unattenuated astronomical shape of the legacy framework, but it is not intended to represent raw, unadjusted station data. Rather, this comparison demonstrates the broad structural differences between a flat, open-ocean calculation model and a localized, shallow-water sieve that incorporates real-world reef friction and tidal pooling.
While this graph helps in seeing how the omission of these adjustments (neap-to-spring, reef attenuation calculation) inflates the heights of an unattenuated open-ocean curve, it is equally easy to discern that the simple addition of 0.43 meters to many of the waveforms in the 2013 legacy analysis itself would have breached the transmitter submersion ceiling (3.45 feet) by July 4, if not earlier. The legacy analysis, indeed the very ability to transmit distress calls after July 4, 1937 from Nikumaroro, only becomes possible if the airplane is able to attain the 1 foot and 4.93 inch elevation. This steep elevation requirement was itself mathematically necessitated by the fact that the legacy analysis relied strictly on unadjusted open-water constants rather than real-world coastal geophysics.
The localized vertical fluctuations, in which the low tides in the ECRAO analysis track both higher and lower than the legacy model’s unadjusted open-ocean baseline, and in which the high tides in the ECRAO analysis consistently track lower than or, infrequently, about the same as the legacy baseline, are the consequence of:
1. the two competing fluid-forcing engines in the ECRAO model, the neap-to-spring tide cycle and the 1D Hydrodynamic Sieve, acting upon the continuous 192-hour timeline, and
2. the legacy model's reliance on unadjusted open-ocean baseline data rather than localized shallow-water geophysics.
The dynamic widening and partial convergence of this vertical gap over the eight-day window illustrate precisely how the application of Courtier’s Form Ratio and the neap-to-spring transition dampens the extreme high-tide surges non-linearly when forced through the 1D Hydrodynamic Sieve, whose methodology is set forth in this accompanying code.
The intervals where the ECRAO low tides plunge lower than legacy's are driven by the pressure of the neap-to-spring transition. This is programmatically captured by the 336-hour non-linear fortnightly modulation wave, which expands the overall tidal range as the astronomical gears advance into the first week of July 1937.
Conversely, the intervals where the ECRAO low tides rest higher than the legacy model's low tides are driven by the damping, or pinching, effect of the application of the downscaling function with Courtier's Form Ratio. By locking this 0.500 attenuation factor into the 1D Hydrodynamic Sieve, the script models the shallow-water pooling phenomenon in which the wide coral shelf acts as a physical dam and hydraulic brake, restricting drainage over the flat rock pavement.
For the complete Python script that made the comparison graph possible, please refer to this link.
Additionally, the legacy model was unable to observe precisely the effects of ionospheric recombination lag, which, at the times at which it occurs, is a fingerprint of the Nikumaroro time zone.[22] This structural deficiency of the legacy timeline ultimately stems from a failure to synchronize the solar grid. While the legacy modelers retained the authentic, historically accurate timestamps logged by the radio receivers, they inadvertently superimposed an incorrect, shifted astronomical horizon directly over those recorded events. By not realizing that they had manually calculated and labeled the astronomical sunrise and sunset boundaries using modern 21st-century administrative time-zone rules, they superimposed a forward-shifted clock canvas directly over the authentic 1937 operational timeline.[23] This framework dragged the day-night boundaries a full 60 minutes too late along that canvas.
The legacy modelers did not notice the effect of this hour-long phase mismatch because their analysis focused primarily on the most credible nighttime signals. Because these high-confidence receptions naturally occurred deep within the midnight block, shifting the solar boundaries by an hour still left those specific data points safely surrounded by darkness on paper, effectively hiding the structural error from view. However, when cross-examined against the laws of solar photoionization across the entire continuous log, this boundary displacement creates a solar day that, while administratively correct, is astronomically incorrect. It shifts the day-night thresholds forward, forcing the earliest transitional evening signals to transmit through late afternoon daylight on paper, or through the 45-minute ionospheric recombination lag zone. This flaw is cleanly resolved by the ECRAO engine.
This mismatch also caused one of the most important receptions, Ray Havens' July 7 report of the same coordinates that Nina Paxton recorded on July 3, to be labeled as "Not Credible." The coordinates were 173°W, 5°S, 107 miles ESE of Nikumaroro. Havens' reception at 6:40 pm Nikumaroro time was received 62 minutes after the actual solar sunset (5:38 pm on Nikumaroro), not, as reported in the catalog, two minutes after sunset. The legacy model judged Havens' signal to have occupied the earliest phase of the 45-minute ionospheric recombination lag zone, too soon for free electrons within the D layer, which are ionized by the sun, to recombine with oxygen ions and allow radio signals to be reflected from the E and F layers above. In fact, Ray Havens' reported signal was 17 minutes past the ionospheric recombination lag zone, received at a time that would otherwise have caused that reception to have been judged as credible beyond a reasonable doubt.
| Analytical Layer | Clock Time | Timekeeping & Database Protocol | Operational & Forensic Significance |
|---|---|---|---|
| Part I: The Authentic 1937 Operational Baseline | |||
| Itasca Base Log | 06:25 PM | Naval Zone Time -11½ (UTC-11:30) |
Astronomical sunset at Howland Island. The ship's wall clock is running exactly 30 minutes fast relative to true sun time at that specific meridian.[24] |
| Longitudinal Delta | -09 minutes | Earth Rotation Constant (1° = 4 Minutes of Solar Transit) |
Nikumaroro sits approximately 2.2 degrees of longitude further east than Howland Island. The physical sun sets at Nikumaroro first. |
| Island Wristwatch Face | 06:16 PM | Un-Shifted Ship Time Tracking | The Clock Face Reality. An Itasca watchman tracking Nikumaroro's longitude under the ship's Zone -11½ protocol would see the hands point here the exact microsecond the sun touched the horizon on Nikumaroro. |
| Administrative Hoist | -30 minutes | Legal Time Zone Offset Removal | Strips away the Navy's advanced scheduling block used to keep the ship's logs synchronized with the flight's radio windows. Drops the dataset symmetrically down to standard, un-hoisted whole-hour Mean Time. |
| Local Apparent Time | 05:46 PM | Represents the sun's position under an idealized, geometric model. | |
| Astronomical Solar Shift | -8 minutes | The Equation of Time (EoT) & Refraction Sieve |
Accounts for the ~4-minute Equation of Time (EoT) solar lag inherent to early July aphelion, combined with the ~5-minute marine atmospheric refraction and solar radius offsets that bend light rays upward. Corrects the timeline to account for the physical variance between theoretical astronomy and visual reality on the water column. |
| Observed Meteorological Sunset | 05:38 PM[25] | The moment the sun clears the geographic horizon. The ultraviolet light source cuts off, and the equatorial D-layer ionospheric molecular recombination 45-minute countdown begins. | |
| Part II: The Legacy Model Mapping | |||
| Normalized Ledger | 06:40 PM | Conversion of Havens' Montana reception to Nikumaroro Time using UTC as an intermediate (UTC-11:00) |
Ray Havens' original 1937 recorded timestamp is mathematically converted to fit a uniform whole-hour spreadsheet column. Numerically, this ledger standard is completely accurate. |
| Anachronism | 06:38 PM[26] | Modern IANA Registry Lookup (Post-1994 IDL Template) |
Legacy modelers consulted standard modern twilight references. The backend registry used the 1995 International Date Line shift, projecting a modern forward-shifted clock face backward into a 1937 sky. |
[1] Britannica Editors, "D region," Encyclopædia Britannica, last updated by John P. Rafferty, accessed August 23, 2026, https://www.britannica.com/science/D-region. ↩
[2] Davies, Kenneth. (1965). Ionospheric radio propagation (National Bureau of Standards Monograph 80). U.S. Department of Commerce, National Bureau of Standards. https://doi.org/10.6028/NBS.MONO.80 pp. 8-12, sec. 1.4.2. (links back to the graph legend in Figure 1.0)
[3] Brandenburg, Bob. 2013. "Time and Tide." TIGHAR Tracks 29, no. 1 (February): 54, accessed August 23, 2026, https://tighar.org/Publications/TTracks/2013Vol_29/TTFeb2013.pdf ↩
[7] The subset of signals at the very peak of high tide were sent at what is known as "slack tide," that point in the tidal cycle at which the waves go silent for a few minutes while the tide prepares to change direction. It would have been an ideal time to transmit, and the nib-like peaks[a] on the graph, where water temporarily chokes and pools during the drainage cycle, seem to show that time was utilized. ↩
[a] These nib-like peaks, alternating between steeper rises with shallower ebbs and shallower rises with steeper ebbs, constitute the exact signature of a restricted coral reef flat system. This highly localized non-linear phenomenon is termed "spring-neap modulation of incident asymmetry" (Nidzieko, N. J., & Ralston, D. K. Tidal asymmetry and velocity skew over tidal flats and shallow channels within a macrotidal estuary. Journal of Geophysical Research: Oceans, 117[C3]. https://doi:10.1029/2011JC007384)
As an aside, two of McMenamy's reported receptions (July 2 and July 3) appear at the exact tidal peak, characterizing spring-neap modulation of incident asymmetry, which in turn defines a slack tide intermission. McMenamy is listed singly on the graph at 3 pm on July 2 and as part of a group of "four amateurs" at 2:30 am on July 3. This new information tends to exonerate McMenamy, who was branded by the U.S. Navy at the time as a hoaxer. His first reported reception on July 2 remains a likely honest poor recollection of the calendar date, and his reported frequency of 3105 kHz may have been caused by the local oscillator in his radio creating a heterodyne of the higher harmonic of the original signal. The reported reception times' coinciding accidentally to the minute to the slack tides' arrivals seems too much of a coincidence to ignore.
[8] "Nikumaroro Island, Phoenix Islands, Kiribati — Sunrise, Sunset, and Daylength, September 1937," Time and Date, accessed August 23, 2026. For a visual verification of the 5:38 pm sunset baseline that bypasses modern database formatting errors, refer to the automated geodetic calculations mapped to the September 1937 seasonal orbital node: https://www.timeanddate.com/sun/@4030922?month=9&year=1937↩
[9] The section concerning the phase lag array is an important component for computing the tidal heights. The five settings look like this: ↩
phases = {
'M2': -1.2,
'S2': 0.1,
'N2': -1.8,
'K1': 0.5,
'O1': -0.4
}
The values in this geomorphic phase lag array are not arbitrary or decoupled fabrications. Rather, they were extracted from a multi-dimensional parameter space, isolated by a machine learning optimization routine that ran against a strict network of physical boundary vectors. Those vectors were defined entirely by constraining the empirical convergence of phase lag values against my inputs of the Lockheed Electra's structural clearances, the invariant orbital speeds of the astronomical constituents, and the permanent geomorphic dimensions of the Nikumaroro reef flat.
In tidal physics, phase lag numbers are permanent physical constants for a specific location. They represent the fixed time lag it takes for an ocean wave to travel across deep water, bend around Nikumaroro's underwater shelf, and climb over the shallow coral reef.
The values in this programming phase array combine the unique astronomical alignments of July 1937 with the invariant geomorphic phase lags native to the Nikumaroro shelf. While the raw programming numbers shift dynamically, and completely predictably, when calculating alternative calendar eras, the underlying physical time delays and the 0.500 Form Ratio constraint remain frozen across centuries as a permanent structural signature of the reef flat itself.
[10] Schrijvershof, R. A., van Maren, D. S., Torfs, P. J. J. F., & Hoitink, A. J. F. (2023). A synthetic spring-neap tidal cycle for long-term morphodynamic models. Journal of Geophysical Research: Earth Surface, 128, e2022JF006799. https://doi.org/10.1029/2022JF006799 ↩
[11] Havens Hears Message from Earhart Plane, The Independent-Observer, Conrad, Montana, 8 July, 1937, p. 1. ↩
[12] Paxton, Nina L., "The Call of a Courageous Lady," undated typescript (internal content references August 10, 1937), Box 1, Folder 1, Nina L. Paxton Papers, 1937-1970, Southern Appalachian Archives, Mars Hill University, accessed August 23, 2026, https://southernappalachianarchives.org/items/show/227. ↩
[13] Note that the tidal generator program has an adjustable temporal variable called "target date," which you can enter to the command line when you run the program. Tidal hindcasts from 1937 up to and including forecasts in the modern era can be achieved with the two core Python scripts, and the graphical output will adjust accordingly. (No graph is produced if the landing is outside of safe landing limits, i.e., > 6 inches of tidal depth on Nutiran, but the file named nikumaroro_projected_tides.csv is always produced, whether a landing by Earhart was possible on that date or not.) ↩
Thus, the accuracy of the tidal generator in this system is inherently verifiable, or, in scientific terms, eminently falsifiable, presuming real-time tidal heights were to be physically measured to professional hydrographic standards on the Nutiran reef flat surface.
This falsifiability is of course limited by secular sea-level rise, which predicts rising sea levels well beyond those that were trended in the 20th century, and long-term amplitude modulations driven by the fact that the lunar and solar gears (the Lunar Nodal Precessional Cycle, lasting 18.6 years) shift somewhat by the end of each one-half cycle (9.3 years). For these reasons, the forecasts generated by this script are not expected to be within stated meteorological tolerances (±6 to 12 inches) beyond 2035. On most calm days, the accuracy should prove far closer than the stated meteorological tolerances.
[14] Kanton Island was chosen over Hull Island, which was used in Bob Brandenburg's previous analysis (2013), because Kanton's dredged ship channel yields a true, un-attenuated, deep-water baseline supported by more than 50 years of continuous, hourly empirical UHSLC tide gauge observations. Utilizing Hull's lagoon-restricted regime would have erroneously compounded localized friction within the downscaling framework (detailed in the script here). Relying on Hull's unadjusted open-ocean baseline data, which was the only foundational datum available from Hull Island for a predictive proxy, would render calculated tidal heights unrealistically high. ↩
Note that for this analysis the proxy island, Kanton, was not used as a direct proxy but rather was used only for computing the amplitude array, consisting of amplitudes of the five major tidal constituents, in the tidal equation.
[15] For more on how tides are classified and reference works consulted in building this algorithm, see:
André-Marie Courtier, "Classification of Tides in Four Types," The International Hydrographic Review 15, no. 1 (1938): 50–58, which defined the universal Form Ratio fraction to use in tidal classification. ↩
Do-Seong Byun and Deirdre E. Hart, "A Monthly Tidal Envelope Classification for Semidiurnal Regimes in Terms of the Relative Proportions of the S2, N2, and M2 Constituents," Ocean Science 16, no. 4 (2020) revived Courtier’s formulas and showed they could be scaled to model multi-day, long-term wave envelopes (LTE), rather than just daily snapshots of tides.
David C. Lay, Steven R. Lay, and Judi J. McDonald, Linear Algebra and Its Applications, 5th ed. (Boston: Pearson, 2016) defined the rules to solve systems of linear equations.
[16] ECRAO is the abbreviation for the model in this paper. It stands for "Empirically Calibrated Reef-Top Attenuation Operator." ↩
[17] Brandenburg, Bob. "Time & Tide," TIGHAR Tracks, Vol. 29, No. 1, February 2013, pp. 53–64. ↩
[18] Ibid., p. 59, Figure 7 ("Taxi and park" spatial distribution mapping relative to Survey Point A baseline datums). ↩
[19] Ibid., p. 54 ("The Electra Landing Area" terrain constraints parameter report). ↩
[21] United Kingdom Hydrographic Office. (2026). "EasyTide FAQs: Frequently asked questions regarding tidal predications and chart datums." ADMIRALTY EasyTide. Retrieved September 18 2026, from https://easytide.admiralty.co.uk/FAQs. UKHO EasyTide deep-water predictions for Hull Island are derived linearly from regional South Pacific baseline standard ports. ↩
[22] Davies, Kenneth. 1990. Ionospheric Radio. Peter Peregrinus Ltd. This physical delay, scientifically defined as ionospheric sluggishness, occurs because the lower D-region cannot dissolve instantly when solar photoionization ceases at dusk. Because intense equatorial solar radiation produces a highly saturated daytime electron population, this chemical recombination process reaches its maximum 45-minute decay threshold in the tropical Pacific. This transient absorption wall must completely clear before low-power, shortwave signals can successfully stabilize for long-distance skywave propagation. Separately, high-frequency harmonic leakage describes how a transmitter natively forces out weaker secondary signals at exact integer multiples of its primary frequency. While the primary wave is smothered by daylight absorption, these shorter harmonic spikes punch through the lower atmosphere to bounce off the higher F2-layer canopy, enabling anomalous daytime transoceanic intercepts, such as Betty Klenck and Nina Paxton reported. ↩
[23] Law, Gwillim. 2001. "Kiribati Time Zones." Statoids. Last modified May 28, 2001. https://statoids.com/tki.html. Note that the history of time zone changes for Nikumaroro can be found on this site by referencing the Pacific / Enderbury zone. ↩
[24] Riley, John P. Jr. 2000. "The Earhart Tragedy: Old Mystery, New Hypothesis" U.S. Naval Institute. https://www.usni.org/magazines/naval-history-magazine/2000/august/earhart-tragedy-old-mystery-new-hypothesis ↩
"Steaming at 14 knots (with sunset at 1825 and sunrise at 0615 ship's time), the 13-hour search would have been completed by about 1130 ship's time on 3 July—the morning after the plane disappeared."
[25] "Nikumaroro Island, Phoenix Islands, Kiribati — Sunrise, Sunset, and Daylength, September 1937," Time and Date, accessed August 23, 2026. For a visual verification of the 5:38 pm sunset baseline that bypasses modern database formatting errors, refer to the automated geodetic calculations mapped to the September 1937 seasonal orbital node: https://www.timeanddate.com/sun/@4030922?month=9&year=1937↩
[26] For a graphical representation of how Figure 1.0 would have appeared if it had been drawn with the legacy sunset and sunrise parameters (6:47 am and 6:38 pm, respectively), click here. Notice that there are several signals on Day 1 that were judged "Credible" but would have been heard, under the legacy regime, while the signal was still in the ionospheric recombination lag zone. Note as well how, if sunset had occurred an hour later than it actually did, Havens' signal would now reside in this ionospheric recombination lag zone. For the modified version of the graphical output code that produced this graph, click here.↩
The title of this paper borrows from that of an important work in the field of information displays and visual thinking, which I consulted often for guidance in setting up the graph:
Tufte, Edward R. Visual Explanations: Images and Quantities, Evidence and Narrative. Graphics Press, 1997.
Note also that I have omitted the reported signals of Arthur Monsees, Frank Freitas, station K6NTV, Ray Mahoney, and the radioman from Peru due to the fact that they forgot exactly when they heard the signal or it was simply poorly documented in news accounts. This exception does not apply to Betty Klenck, whose notebook, while not a time-stamped chronology, is the only real-time transcription of distress calls that has surfaced from the week of July 2, 1937.
Special thanks are due to Andrew McKenna, board member of TIGHAR, and to Kenton Spading, for their valuable suggestions for improving this article.
Looking shoreward towards Nutiran, the possible landing site of Amelia Earhart's Lockheed Model 10-E Electra, this photo was taken in the late afternoon of July 5, 2017, 80 years and three days after Amelia Earhart's disappearance. The tide is high in the photo. At that exact time and date in 1937, the tide would have hovered between 2.632 and 2.68 feet. The rusted, sunken boilers of the SS Norwich City are visible in the background. Photo by Joe Cerniglia. Licensed for open-science redistribution under the terms of the GNU General Public License v3 [GPLv3]).
Brandenburg, B. (2013). Time and tide: A catalog and analysis of radio signals during the search for Amelia Earhart. The International Group for Historic Aircraft Recovery (TIGHAR) Monograph Series.
Byun, D. S., & Hart, D. E. (2020). A monthly tidal envelope classification for semidiurnal regimes in terms of the relative proportions of the S2, N2, and M2 constituents. Ocean Science, 16(4), 939–962. https://doi.org/10.5194/os-16-965-2020
Courtier, A. M. (1938). Classification of tides in four types. The International Hydrographic Review, 15(1), 50–58.
Davies, Kenneth. (1965). Ionospheric radio propagation (National Bureau of Standards Monograph 80). U.S. Department of Commerce, National Bureau of Standards. https://doi.org/10.6028/NBS.MONO.80
Davies, Kenneth. (1990). Ionospheric Radio. IEE Electromagnetic Waves Series, 31. London: Peter Peregrinus Ltd. on behalf of the Institution of Electrical Engineers (IEE). https://doi.org/10.1049/PBEW031E_fm
Lay, D. C., Lay, S. R., & McDonald, J. J. (2016). Linear algebra and its applications (5th ed.). Boston, MA: Pearson.
Nidzieko, N. J., & Ralston, D. K. (2012). Tidal asymmetry and velocity skew over tidal flats and shallow channels within a macrotidal estuary. Journal of Geophysical Research: Oceans, 117(C3), C03001. https://doi:10.1029/2011JC007384
Schrijvershof, R. A., van Maren, D. S., Torfs, P. J. J. F., & Hoitink, A. J. F. (2023). A synthetic spring-neap tidal cycle for long-term morphodynamic models. Journal of Geophysical Research: Earth Surface, 128(2), e2022JF006799. https://doi.org/10.1029/2022JF006799
