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 - 8, 1937:
Note: This forensic timeline contains fine details; pinch-zooming will aid in seeing these details more clearly.
The airplane in the graph (inverted red triangle) must land no later than hour 11.0095 (11:01 am Nikumaroro time) with a tidal height of exactly 0.4967 feet (5.96 inches), 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.[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, sitting within very close approximations of the actual astronomical times for 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 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
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_1937_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 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 Niku.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. It will generate your tides csv, which contains all the tidal data you need for the graph. 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 tidal heights over a 54-year period for Kanton Island.[13] You will need to modify the Python solver script in line 19 to represent where you stored the tidal history file when you downloaded it.
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. It will generate your tides csv, which contains all the tidal data you need for the graph. 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 tidal heights over a 54-year period for Kanton Island.[13] You will need to modify the Python solver script in line 19 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.[14]
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 168 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.
Last, here is the Python script that produces the pdf and the csv.
Endnotes
[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.
[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
[4] Ibid., 58-60.
[5] Ibid., 58-60.
[6] Ibid., 58-60.
[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] "Sunrise and Sunset Times in United States," Time and Date, accessed August 23, 2026, https://www.timeanddate.com/sun/@4030922.
[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.
[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] 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 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.
[14] For more on how tides are classified, 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.
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.
⁓⁓⁓ ❀ ⁓⁓⁓
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]).
Bibliography
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, K. (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
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
