The Flood's Water Budget

No young-earth model has the Flood covering Everest; all raise today's mountains late in the Flood, and the water is today's ocean. That answer has an unstated price: a pre-Flood earth with 8.6 km less relief, rebuilt in a year against measured mantle viscosity. Every proposed new-water source is under a per cent of an ocean, bar Brown's rejected chamber.

Draft:  September 2026

"if the entire earth's surface were levelled by smoothing out the topography of not only the land surface but also the rock surface on the ocean floor, the waters of the ocean would cover Earth's surface to a depth of 2.7 kilometres (1.7 miles)." — Creation Ministries International, The Creation Answers Book1

"How high were the mountains before the Flood? We don't know". — the same chapter, one page later1

"For these reasons I conclude that water depths of only a few hundred meters are more likely than those of one or two kilometers or more." — John Baumgardner, author of catastrophic plate tectonics, 20122

Summary

Genesis 7 says the water rose until "all the high mountains under the whole heaven were covered" and stood fifteen cubits above them.  No young-earth model reads that as water over today's mountains.  Every one of them has today's ranges rising late in the Flood or after it; in catastrophic plate tectonics the Himalaya rise when India meets Asia near the end of the Flood year, and Baumgardner's own isostasy note prices the uplift.3  The water that covered the pre-Flood mountains is, on every model, today's ocean.  So the two arithmetic questions are not "where did three extra oceans come from" but what the pre-Flood earth had to look like for today's water to cover it, and what it costs to rebuild that earth into this one in a year.  The young-earth literature has addressed both for sixty years, and this article prices every answer against the earth's measured inventory of water and its measured shape.  The heat side of the same models is in The Heat Problem; the plate-tectonic mechanism is in Catastrophic Plate Tectonics.

The findings, stated first.

  1. There is no spare water, which is why every model flattens the earth instead. Every reservoir outside the ocean, all the ice, all the groundwater, every lake, river, swamp and the entire atmosphere, comes to 4.8 × 10⁷ cubic kilometres, which would raise the sea 127 metres.4 For scale only: covering today's topography to Everest plus fifteen cubits would take 3.3 more oceans.5 No model claims that, and none needs to, because all of them raise the mountains after the water is already there. The requirement that follows is in point 5.
  2. The vapour canopy was never a water source, and its builders said so. Dillow's own footnote: "most of the water of the Deluge came from the fountains of the deep". Vardiman's conversion prices every canopy ever proposed: one that doubles the surface pressure holds about ten metres of water, 0.4 per cent of the ocean. Both major ministries have dropped it.
  3. The fountains of the deep have one explicit volume in the whole literature, and it is Walt Brown's. His subterranean chamber is 54 per cent of the ocean. The one peer-reviewed magmatic estimate, corrected for its author's factor-of-ten slip, is 9 per cent. Everything else is recycled seawater.
  4. The mantle holds oceans of water, and it is not a way out. The water is hydroxyl bound in crystal lattices at 400 to 660 kilometres depth. Releasing one ocean of it means melting 1.4 × 10²³ kilograms of rock, a thirtieth of the mantle, at a minimum heat cost of 7 × 10²⁸ joules, seven times Baumgardner's own figure for runaway subduction.6
  5. The only coherent young-earth answer is that the water never left. CMI and Snelling both say it: the ocean is the Flood water, and the basins deepened to hold it. CMI gives the right number for a smoothed earth, 2.7 kilometres. What follows is a requirement no young-earth source states: the pre-Flood earth's relief, measured as peak height plus basin depth, had to be about 8.6 kilometres less than today's.5 Not Snelling in 1,100 pages, not Clarey's five-continent stratigraphy, not AiG or CMI, gives a pre-Flood ocean volume, a pre-Flood mountain height, or a pre-Flood distribution of elevation.
  6. The tectonic lever is real, small and slow. Hot new ocean floor stands higher than old floor. Replacing every square kilometre of seafloor with brand-new ridge crest, an upper bound no model reaches, raises the sea 2.0 kilometres. The observed Phanerozoic maximum is 100 to 170 metres, over tens of millions of years. The Flood needs 17 metres a day, 160,000 times the fastest sea-level rise the earth has demonstrably produced.7
  7. The model's author withdrew the lever, and the ministries still print it. Baumgardner in 2012: "perhaps only 100-200 m of sea level rise above the pre-Flood sea level may have been involved." Clarey's 2023 conference paper still cites 1.6 to 2.0 kilometres from Baumgardner 1986; CMI's Answers Book still prints 2,000 metres. Baumgardner's own final position is a few hundred metres of fast, shallow water, which is not the Flood Snelling or CMI describe.
  8. The solid earth cannot rearrange itself in a year. Post-glacial rebound measures the mantle's viscosity, and at that viscosity a continent-scale load relaxes in thousands of years. the claim that mountains rose and valleys sank in twelve months requires a mantle some four thousand times less viscous than the one that is measured.7

The verdict.  The young-earth answer that survives arithmetic is the modest one:  the water is today's ocean, and the Flood earth was flatter.  Taken to its conclusion, that means a pre-Flood world with almost no relief, its highest ground within a hundred or two hundred metres of sea level, followed by the raising of every mountain range and the sinking of every ocean basin in one year against a measured mantle viscosity that forbids it.  The literature has never stated the requirement, let alone met it.  Where it has tried to add water, the canopy, magma, the mantle, its own authors' numbers fall short by a hundredfold or more, and the models that supplied a large tectonic sea-level rise have been withdrawn by the man who built them.

Part 1: The requirement

How much water there is.  The ocean holds 1.332 × 10⁹ cubic kilometres, at a mean depth of 3,682 metres, and "Approximately 97% of the world's water reserves exist in the ocean."8  The rest, by the standard inventory, is ice (24 million cubic kilometres), groundwater (23 million), and a scatter of lakes, soil moisture, swamps, rivers and air that together do not reach a million.9  The atmosphere holds 12,900 cubic kilometres, which spread over the globe is 25 millimetres of rain.4

The shape of the earth.  The solid surface is bimodal.  NOAA's description of the hypsographic curve:  "two primary elevation groupings: the continents, several hundred meters above sea level, and the oceanic abyssal plains, roughly 4,300 meters below sea level."10  Seventy-one per cent of the surface is below sea level; less than one per cent is above 3,000 metres.  Level the whole surface to a sphere and the present ocean stands 2.6 kilometres deep everywhere.5  That is the figure CMI quotes, and it is right.

Why every model flattens the earth.  The young-earth position, stated by all three ministries, is that today's mountains did not exist when the water rose.  CMI:  today's mountains "were formed only towards the end of, and after, the Flood by collision of the tectonic plates and the associated upthrusting".1  Baumgardner's 2005 note prices the mechanism:  thickening continental crust from 35 to 60 kilometres raises the surface about 14,500 feet.3  The Everest figure below is therefore not a claim about any model.  It is the reason the models say what they say.  The hypsometry was recomputed for this article from NOAA's 2022 one-arc-minute relief model, and the script is published with it.5  To raise the sea to Everest plus fifteen cubits over today's topography would take 5.7 × 10⁹ cubic kilometres of standing water, 4.3 times the present ocean; the extra 4.4 × 10⁹ is 3.3 oceans, and there is no such water on the planet.  Lower the pre-Flood mountains to one kilometre and the extra water needed, with today's basins, is still a third of an ocean.  So the models must lower the mountains and shallow the basins together.  Put it another way.  Define effective relief as the height of the highest peak plus the mean basin depth weighted by ocean area, less the mean land elevation weighted by land area.  Today that is about 11,200 metres.  The present ocean can cover an earth whose effective relief is 2,600 metres.  A Flood covered by today's water needs the pre-Flood earth flattened by 8.6 kilometres.  The hypsometric curve is brutally nonlinear:  adding a second entire ocean raises the sea only 2.8 kilometres, because by then the water is spreading over a globe that is 98 per cent flooded.5

Part 2: Where the young-earth literature gets the water

The canopy, which its own builders priced.  The oldest answer is that a shell of water vapour above the pre-Flood atmosphere, the "waters above" of Genesis 1:7, fell as the forty days of rain.  Joseph Dillow's 1981 book is the fullest statement, and its own footnote gives the game away:  "most of the water of the Deluge came from the fountains of the deep (Gen. 7:11)."11  The reason is thermodynamic.  Water vapour is a greenhouse gas, and a canopy heats the surface beneath it.  Rush and Vardiman modelled it at the 1990 International Conference on Creationism:  "only 50 mb of water vapor added above the present atmosphere would raise the surface temperature as determined by a radiation balance from 320 K to 409 K."12  Fifty millibars is twenty inches of water.  Their reply to a critic conceded the consequence:  "our 50 mb canopy (20 inches of precipitable water) would hardly provide 40 days and nights of heavy rainfall."12  Vardiman and Bousselot pushed every parameter in the canopy's favour in 1998 and concluded that the water content "could possibly be raised to as much as 1.0 meter. ... Unfortunately, this amount of water in a canopy would not contribute significantly to the waters of the Genesis Flood".13  Vardiman's 2003 paper states the conversion that prices every canopy ever proposed:  a canopy of 1,013 millibars, one that doubles the surface pressure, holds 10.13 metres of water.14  That is 0.4 per cent of the ocean.  The canopy was arithmetically hopeless before it was thermally hopeless.  Creation Ministries International lists it among arguments creationists should not use,15 and Answers in Genesis's 2026 statement puts the physics in one line:  "The sun doesn't have a dimmer switch."16

The fountains of the great deep.  The Flood model of every major ministry now puts the water source in the "fountains of the great deep" of Genesis 7:11, read as water from below.  In catastrophic plate tectonics the fountains are steam jets at the spreading ridges, which the 1994 founding paper says "should provide adequate water to explain up to 150 days of open 'windows of heaven'".17  Steam jets recycle ocean water; they do not add any.  The one attempt to price genuinely new water from below is Hamilton Duncan's 2010 paper on volcanic degassing, which assumes every large igneous province and oceanic plateau on earth erupted in the Flood year and released its dissolved water, and reports "at least 58 cm of rain worldwide every day for forty days."18  His mass figure, 1.19 × 10²³ grams, is internally consistent; his final division is wrong by ten.  That much water is 233 metres over the globe, or 583 centimetres a day.19  Corrected, it is the largest new-water figure in the peer-reviewed young-earth literature, and it is 9 per cent of the ocean.

Walt Brown's hydroplate theory is the only model that states an explicit volume:  a subterranean chamber of 7.15 × 10²³ cubic centimetres,20 which is 1,400 metres of water over the whole globe and 54 per cent of the present ocean.  Snelling's Earth's Catastrophic Past rejects the chamber, and Baumgardner rejects the physics.  Even granted, a smoothed earth with Brown's chamber added is under 4 kilometres of water, still 4.8 kilometres short of Everest.

The mantle.  The newest source is the water bound in mantle minerals.  When a diamond containing hydrous ringwoodite was reported in 2014, Andrew Snelling, quoted in an Answers in Genesis article, wrote that the find "confirms the capacity of the mantle to have housed the water that was released when the fountains of the great deep were broken up to commence the Flood, and the huge volume of water that was released through these fountains for as much as 150 days, providing more than enough water to help submerge the whole globe".21  Part 4 takes this up.  The short answer is that the "water" is hydroxyl in a crystal lattice at 400 to 660 kilometres depth and 1,500 kelvin, and releasing an ocean of it means melting the mantle that holds it.

Part 3: Where the young-earth literature puts it afterwards

The sink is the coherent part.  Both Snelling and CMI say plainly that the water never left.  CMI's Answers Book:  "if the entire earth's surface were levelled by smoothing out the topography of not only the land surface but also the rock surface on the ocean floor, the waters of the ocean would cover Earth's surface to a depth of 2.7 kilometres (1.7 miles). ... Quite clearly, then, the waters of Noah's Flood are in today's ocean basins."1  Snelling:  "the overall result of the Flood was that most of the Flood waters remained on the earth. ... This, in turn, implies three possibilities: either the proportion of land area to water area was larger before the Flood; the ocean basins were shallower before the Flood" or both.22  The 2.7 kilometre figure is correct.  So is the logic:  today's ocean covers today's earth to that depth if the earth is flattened, so a Flood that covered everything needs an earth that was flatter, not more water.  What no source supplies is the size of the flattening.

The pre-Flood earth, without a number.  Asked how the water covered the mountains, CMI answers:  "How high were the mountains before the Flood? We don't know; we can't tell by looking at today's mountains because they were formed only towards the end of, and after, the Flood".1  Answers in Genesis:  "This pre-Flood world had shallower seas (no deep ocean trenches) and lower mountains".23  Snelling names three possibilities and quantifies none.  No creationist source found for this article gives a pre-Flood ocean volume, a pre-Flood mean mountain height, or a pre-Flood distribution of elevation.  Part 4 gives the number they would need.

The sea-level mechanism its author withdrew.  Catastrophic plate tectonics offered a quantitative sink and source in one:  hot new ocean floor stands higher than cold old floor, so replacing the floor lifts the sea onto the land, and cooling it afterwards drops the sea back.  Baumgardner's 1986 paper computed it:  "we obtain an increase in the height of the ocean bottom as the old lithosphere is replaced of 2,500 m."24  His abstract reported that as sea-level rise, which it is not; ocean-floor uplift spreads over the whole globe once the water floods the land.  In 2012 he withdrew it:  "Whereas I once thought that perhaps as much as 1000-1500 m may have occurred, more recently I have come to suspect that the overall changes in sea level were likely much more modest. ... So my present guess is that perhaps only 100-200 m of sea level rise above the pre-Flood sea level may have been involved."2  And:  "While I once believed a rise in global sea level of several hundred meters or more was needed to account for the sedimentation and erosion patterns on the continents, I am no longer convinced this is so."2  What replaces it is "large amplitude, high velocity tsunami-like waves" from a rotationally unstable earth, "with only small overall changes in sea level."2  The withdrawal has not propagated.  Clarey and Werner's 2023 conference paper still reports that "Creationists have calculated that this elevated seafloor could have raised the global sea level by 1.6 kilometers (Snelling 2014c) to 2.0 kilometers (Baumgardner 1986)".25  CMI's Answers Book still prints up to 2,000 metres.

Baumgardner's own final position is shallow water.  Asked directly how deep the water stood over the continents, he answered:  "I want to be forthright here in saying that I have no means by which I can with any degree of confidence put tight quantitative constraints on the water depth over the continents during the Flood. ... For these reasons I conclude that water depths of only a few hundred meters are more likely than those of one or two kilometers or more."2  He needs fast, shallow water to erode; deep water is slow water.  Snelling has the water at least seven metres over every pre-Flood mountain;22 CMI has it over Everest-equivalents; the model's builder has a few hundred metres of cavitating sheet flow.  These are different Floods.

Drainage has a vocabulary and no physics.  Tas Walker's 1994 scheme names the stages every later author uses:  "The first stage, during which the waters 'rose and increased greatly' until the whole earth was covered [Gen 7:18], has been called the Inundatory Stage. The second stage during which the waters receded from the earth [Gen 8:3,5] has been designated the Recessive Stage."26  The event that starts the drainage, the "Abative Action", is "assumed to mean an intense world-wide disturbance which started the waters receding from the land".26  The paper contains no water volume, no sea level, no depth and no elevation change.  Oard's sheet-flow and channelised-flow phases are landform arguments in the same frame.  The one quantitative piece is Baumgardner's 2005 isostasy note:  thickening continental crust from 35 to 60 kilometres raises the surface about 14,500 feet.3  The arithmetic is right, and it raises mountain belts, which is where crust thickens.  It does not drain Kansas.

Part 4: What the earth's physics allows

The mantle water, priced.  The mantle really does hold water.  Pearson and colleagues' 2014 diamond inclusion is "direct evidence that, at least locally, the transition zone is hydrous, to about 1 weight per cent",27 and Ni and colleagues' review puts "perhaps several times the mass of the entire hydrosphere" in the earth's interior.28  But the form matters:  "nominally anhydrous minerals (NAMs) in the silicate Earth host a significant amount of water by accommodating H point defects in their crystal lattices."28  There is no liquid.  The water leaves the rock when the rock melts, and it partitions into the melt.  To release one ocean's mass, 1.4 × 10²¹ kilograms, from rock holding one per cent water by weight, 1.4 × 10²³ kilograms of mantle must melt, which is 3.4 per cent of the whole mantle and twenty-eight times the volume of the ocean.  The latent heat of fusion alone is about 7 × 10²⁸ joules, before any of the rock is warmed to its melting point.6  That is seven times the 10²⁸ joules Baumgardner assigns to runaway subduction, a figure the TalkOrigins archive already notes "is more than enough to boil off all the oceans."29  Nor is the exchange fast.  Slabs carry water into the mantle today at a rate worth "roughly ~1 m/m.y. of eustatic sea-level drop if unbalanced by mantle degassing."30  Moving one ocean at the gross flux takes over a billion years.  The Answers in Genesis claim that the ringwoodite find shows the mantle "providing more than enough water to help submerge the whole globe" confuses a reservoir with a source.  It also contradicts Snelling's own book, which argues that little new water was needed.

The tectonic lever, priced.  Ocean floor subsides as it cools, by a law calibrated on the whole ocean:  Stein and Stein's model gives new ridge crest at 2,600 metres and old floor at an asymptote of 5,651 metres.31  Today's floor averages 64 million years old.32  Replace all of it with zero-age crest, a bound no model reaches because new floor cannot be everywhere at once, and the basins lose 9.2 × 10⁸ cubic kilometres of capacity; run through the hypsometry, sea level rises 2,006 metres and floods 97 per cent of the globe.7  That is the ceiling on "the ocean floor rose".  What the record shows is far less.  Miller and colleagues:  "we conclude that sea level in the Late Cretaceous was 100 ± 50 m higher than it is today."33  Müller and colleagues, at the generous end, "170 (85 to 270) meters higher".34  Conrad's review closes the budget for the 230 metres of fall since then, with ridge-volume decrease supplying about 250 metres of it over a hundred million years.30  The mainstream dispute about the Cretaceous highstand runs from 40 to 250 metres.  The requirement is 8,848.

The rate.  Genesis has the water rise over forty days and prevail for 150.  A 2,620-metre stand in 150 days is 17.5 metres a day.  The fastest sea-level rise the earth has demonstrably produced is meltwater pulse 1A at the end of the last ice age, "≥40 mm⋅y⁻¹".35  The Flood needs 160,000 times that.  Conrad's ridge lever runs at metres per million years.7

The solid earth's speed limit.  Mountains rising and valleys sinking is a demand on the mantle's viscosity, which is measured.  Post-glacial rebound, the earth's slow recovery from the weight of the ice sheets, fixes the upper mantle near 1.5 × 10²⁰ pascal-seconds and the lower mantle at 2 × 10²¹ or higher.35  At those values a continent-sized load relaxes in thousands of years, about 4,100 at the standard value and about 600 at Lambeck's lowest.  To do it in one year the mantle must be thousands of times less viscous than the rebound data allow.7  Baumgardner's runaway subduction lowers viscosity locally by heating; the requirement here is global and sustained, at continental wavelengths, and nobody has computed it from his model.  The flood water itself also loads the crust:  three kilometres of water depresses the floor beneath it by about a kilometre, so the sea-level accounting must include the basins sinking under the weight of the very water being added.

The drainage.  Draining 3.3 × 10⁸ cubic kilometres off the continents in 150 days is a mean discharge of 2.6 × 10¹⁰ cubic metres a second, about 120,000 Amazons running for five months.  A sheet flow a kilometre deep on a gentle slope exerts a bed shear competent to roll boulders twenty metres across.7  The young-earth literature treats planation surfaces and water gaps as the signature of that flow.  The mainstream point, made qualitatively by Isaak, is why the Channeled Scablands of Washington, the record of one glacial lake draining, are a regional curiosity rather than the condition of every continent.29

The canopy's physics, for completeness.  A canopy holding a smoothed-earth Flood puts 254 atmospheres on the surface, and condensing it releases 3 × 10²⁷ joules, enough to warm the whole ocean by 500 kelvin.4  The atmosphere as it is holds 25 millimetres of water; to deliver a 2,620-metre stand in forty days it would have to fill and empty completely every 33 seconds.

Where the young-earth side can press.  NOAA's own note on the hypsographic curve concedes something a creationist may fairly quote:  "The dramatic steepening of the hypsographic curve at mountains and oceanic trenches can only be maintained by a dynamic Earth. On geologic timescales, such features would quickly erode or fill in with sediments."10  That is true, and the mainstream answer is uplift and subduction at measured rates of millimetres a year, which is what the plate-tectonics article documents.  It is an argument about how relief is maintained.  It is not an argument that relief can be created and destroyed in a year.

Objections and responses

"The water is still here; the ocean basins simply deepened."  Agreed, and this is the only coherent young-earth answer.  Its cost is stated in Part 1:  a pre-Flood earth flattened by 8.6 kilometres of effective relief, then rebuilt to today's shape in one year against a measured mantle viscosity.  No young-earth source has put a number on the flattening.

"No creationist says the Flood covered Everest; the Himalaya rose at the end of the Flood."  Correct, and this article does not say otherwise.  Every model has today's ranges rising late, and the Everest figure appears here only to show why.  The question the models owe an answer to is how low the pre-Flood mountains and how shallow the pre-Flood basins were.  If the pre-Flood land lay everywhere within a hundred or two hundred metres of sea level, today's water covers it with no extra water at all.  That is a strong result for the young-earth side and nobody has claimed it, because it means a pre-Flood world with no mountains, which is not what Genesis 7:19–20's "high mountains" or the creationist reading of pre-Flood geology describes.  Anything between "flat" and "today" has to be stated, and then the rebuilding has to be paid for against the mantle's measured viscosity.

"The fountains of the great deep supplied the water."  Steam jets recycle the ocean.  The only quantified new-water sources are Duncan's degassing at 9 per cent of an ocean, corrected, and Brown's chamber at 54 per cent, which the other models reject.  Neither closes the relief budget even with a smoothed earth; Brown's chamber added to a flat earth still leaves a 4.8 kilometre deficit against today's relief.

"The mantle holds several oceans."  As hydroxyl in hot rock.  One ocean out costs a thirtieth of the mantle melted and 7 × 10²⁸ joules.

"Rising seafloor pushed the sea onto the land."  Its author now puts the effect at 100 to 200 metres, and the physical ceiling with every square kilometre of floor brand new is 2 kilometres.

"Even the scientists disagree about ancient sea levels."  The disagreement is 40 to 250 metres over tens of millions of years, against a requirement of nearly nine kilometres in a year.

"Genesis says fifteen cubits, not kilometres."  Fifteen cubits above the highest mountains.  The article does not quarrel with the text; it prices what the text requires.  Brown is the one author who reads the fifteen cubits as a uniform clearance and proposes a mechanism, crustal buoyancy equalising the peaks, to produce it.20  The mechanism is asserted, not calculated.

Issues and unanswered questions

  • No creationist has published a pre-Flood hypsometric curve. Clarey's compilation of thousands of stratigraphic columns could in principle be inverted for the volume of relief removed; ICR has the data and has not done it.
  • The integral of Baumgardner's 2012 uplift formula over the actual area and age structure of Flood-year seafloor has not been published by anyone; it is bounded near 700 metres and probably a few hundred.
  • The Ark's draft against the wave amplitudes of Baumgardner's tsunami model has never been put on one page. His "few hundred metres" of cavitating water and the Ark's survival are in tension.
  • Baumgardner's runaway-subduction viscosity field has not been converted to a relaxation time for a continental load.
  • The persistence of steep topography, which NOAA concedes needs active maintenance, deserves the measured uplift and denudation rates stated beside it; this article points to the plate-tectonics article for them.

Verdict

Today's water, on today's earth, stands 2.6 kilometres deep if the earth is flat and covers 71 per cent of it if the earth is not.  Every source of new water in the young-earth literature has been priced by its own proponents or by this article, and the total is a fraction of an ocean against a need for three.  The mantle's water is real and locked in rock.  The tectonic lever is real and two orders of magnitude too small, and its author has withdrawn it.  What is left is the honest answer both major ministries give, that the water never left and the land was lower, and that answer, followed through, requires a world without high ground followed by a year in which the mantle behaved as no measurement says it can.  The literature has never stated that requirement.  It should.

What would change this verdict.  A published pre-Flood hypsometric curve whose effective relief is under 2.6 kilometres, consistent with the sediment volumes the same authors map.  A mechanism releasing an ocean of mantle water without melting the mantle.  A relaxation-time calculation from a young-earth viscosity model that delivers continental uplift in a year.  None exists.

Further reading

Sources

  1. 1.

    Batten, Don et al.  “Noah's Flood — what about all that water?”  The Creation Answers Book, 169–178.  Creation Ministries International.  n.d.  Chapter 12 of a popular young-earth book of answers to common questions, from Creation Ministries International, a young-earth ministry.  It takes the water from Genesis 7:11 and 7:12 and from the ocean-floor uplift of up to 2,000 metres that catastrophic plate tectonics proposes.  The article uses it as the clearest young-earth statement of the water budget, and of its statement that the pre-Flood height of the mountains is unknown.

    1. 1a.

      Page 175:  “Indeed, if the entire earth's surface were levelled by smoothing out the topography of not only the land surface but also the rock surface on the ocean floor, the waters of the ocean would cover Earth's surface to a depth of 2.7 kilometres (1.7 miles). … Quite clearly, then, the waters of Noah's Flood are in today's ocean basins.”  Page 171 still gives the ocean-floor uplift as "up to 2,000 metres". ↩ ↩

    2. 1b.

      Page 176:  “How high were the mountains before the Flood? We don't know; we can't tell by looking at today's mountains because they were formed only towards the end of, and after, the Flood by collision of the tectonic plates and the associated upthrusting.” ↩ ↩ ↩

  2. 2.

    Baumgardner, John R.  101 Questions and Answers Concerning Catastrophic Plate Tectonics.  Self-published.  Apr 2012.  A set of 101 questions and answers in which John Baumgardner, the author of the catastrophic plate tectonics model, replies to questions from a peer review panel of ten scientists.  The review ran from early 2009 to the summer of 2011.  The article uses it for his latest word on the sea-level rise and the water depth, where he retreats from figures he once gave.

    1. 2a.

      Section Q31, page 65:  “Whereas I once thought that perhaps as much as 1000-1500 m may have occurred, more recently I have come to suspect that the overall changes in sea level were likely much more modest. … So my present guess is that perhaps only 100-200 m of sea level rise above the pre-Flood sea level may have been involved.” ↩

    2. 2b.

      Section Q52, page 96:  “While I once believed a rise in global sea level of several hundred meters or more was needed to account for the sedimentation and erosion patterns on the continents, I am no longer convinced this is so.”  And:  “such rotational instability causes large amplitude, high velocity tsunami-like waves to sweep over the continents with only small overall changes in sea level.” ↩ ↩

    3. 2c.

      Section Q94, page 145:  “I want to be forthright here in saying that I have no means by which I can with any degree of confidence put tight quantitative constraints on the water depth over the continents during the Flood. … For these reasons I conclude that water depths of only a few hundred meters are more likely than those of one or two kilometers or more.” ↩ ↩

  3. 3.

    Baumgardner, John.  “Recent Rapid Uplift of Today's Mountains.”  ICR Impact (381).  Mar 2005.  A short popular article in the Impact series of the Institute for Creation Research, by a geophysicist at the institute's graduate school.  It relies on Ollier and Pain's book The Origin of Mountains, and says the ranges were nearly flat and near sea level before their recent uplift began.  The article uses it for the isostasy arithmetic that prices how far thickened crust lifts the surface.

    1. 3a.

      Page ii:  “relative to a region with a 35 km crustal thickness, a zone with a 60 km crustal thickness, for the densities quoted above, would have”.  The sentence goes on: a surface about 14,500 feet higher under isostatic equilibrium. ↩ ↩ ↩

  4. 4.

    Computed for this article in research/physical-constraints.md, C13 and C14, from the USGS/Shiklomanov table:  all non-ocean reservoirs total 4.798 × 10⁷ km³, which through the hypsometry raises sea level 127.4 m.  The atmosphere's 12,900 km³ over 5.1007 × 10⁸ km² is 25.3 mm; a 2,620 m stand needs 103,600 atmospheric turnovers, 2,590 a day over forty days.  A canopy holding 2,620 m of water exerts 254 atmospheres and releases 3.02 × 10²⁷ J of latent heat on condensing, against an ocean heat capacity of 5.76 × 10²⁴ J/K. ↩ ↩ ↩

  5. 5.

    Computed for this article from NOAA's ETOPO 2022 60-arc-second global relief model (doi:10.25921/fd45-gt74, public domain), decoded and integrated by the script bin/etopo-hypsometry.ts; the working is in research/physical-constraints.md, computations C1 to C6.  The integration reproduces the published surface area, ocean volume and mean depth.  Results:  smoothed-earth ocean depth 2,612 m with Charette and Smith's volume; standing water to reach Everest + 15 cubits over present topography 5.72 × 10⁹ km³, extra 4.40 × 10⁹ km³ (3.3 oceans); extra water with all land lowered to 1 km, 4.35 × 10⁸ km³; adding one whole ocean raises sea level 2,836 m; effective relief today about 11,210 m against 2,611 m coverable by the present ocean, a deficit of 8,599 m. ↩ ↩ ↩ ↩ ↩

  6. 6.

    Computed for this article in research/physical-constraints.md, C7 to C9.  Ocean mass 1.377 × 10²¹ kg; at 1 wt % water in the rock, 1.38 × 10²³ kg of mantle must melt, 3.4 % of the 4.01 × 10²⁴ kg mantle; latent heat of fusion about 5 × 10⁵ J/kg gives 6.9 × 10²⁸ J before sensible heating.  At Ni et al.'s gross slab flux of about 10¹² kg/yr, one ocean mass takes 1.38 × 10⁹ years. ↩ ↩

  7. 7.

    Computed for this article in research/physical-constraints.md, C4, C10 to C12 and C15.  GDH1 with every square kilometre of floor at zero age removes 2.553 km × 3.616 × 10⁸ km² = 9.23 × 10⁸ km³ of basin capacity, which raises sea level 2,006 m.  A 2,620 m stand in 150 days is 17.5 m/day, 160,000 times MWP-1A's 40 mm/yr.  Airy loading:  a water column depresses the crust by 1,030/3,300 = 0.31 of its thickness.  Relaxation time τ = 4πη/(ρgλ) for a 3,000 km load is about 4,100 yr at η = 10²¹ Pa s and about 600 yr at 1.5 × 10²⁰.  Draining 3.34 × 10⁸ km³ in 150 days is 2.6 × 10¹⁰ m³/s; a 1,000 m sheet flow on a 10⁻³ slope gives bed shear ρgHS ≈ 9,800 Pa. ↩ ↩ ↩ ↩ ↩ ↩

  8. 8.

    Charette, Matthew A., and Walter H. F. Smith.  “The Volume of Earth's Ocean.”  Oceanography 23(2):112–114.  2010.  A research article that recalculates the ocean's volume from a seafloor map built from satellite data and ship soundings, because ocean volume had not been re-examined in over 25 years.  It finds 1.332 billion cubic kilometres and a mean depth of 3,682 metres, 21 to 51 metres shallower than the most cited earlier estimates, and it notes that less than 10 per cent of the seafloor has been mapped by ships.  The article uses those figures for the ocean's volume and mean depth.

    1. 8a.

      Page 112:  “Approximately 97% of the world's water reserves exist in the ocean.”  Page 113:  “This analysis resulted in a mean ocean depth value of 3682 m.”  “our estimate of 1.332 x 10^9 km3”. ↩

  9. 9.

    U.S. Geological Survey Water Science School.  Where is Earth's Water?  2018.  A water-science web page from the U.S. Geological Survey that reproduces Shiklomanov's 1993 inventory of Earth's water, in cubic kilometres: oceans 1,338,000,000; ice caps, glaciers and permanent snow 24,064,000; groundwater 23,400,000; ground ice and permafrost 300,000; lakes 176,400; soil moisture 16,500; atmosphere 12,900; swamps 11,470; rivers 2,120; biological water 1,120.  The article takes its figures for everything outside the oceans, ice and groundwater above all. ↩

  10. 10.

    Eakins, B. W., and G. F. Sharman.  Hypsographic Curve of Earth's Surface from ETOPO1.  NOAA National Geophysical Data Center, Boulder.  2012.  A data product from the NOAA National Geophysical Data Center in Boulder.  The hypsographic curve shows how much of Earth's surface lies at each height above or below sea level, and this one is computed from ETOPO1.  The article uses it for the two-level shape of the solid surface, and for NOAA's comment on what keeps that shape from wearing away.

    1. 10a.

      Page 1:  “The histogram reveals two primary elevation groupings: the continents, several hundred meters above sea level, and the oceanic abyssal plains, roughly 4,300 meters below sea level. This distribution indicates that the crust of the ocean floor is fundamentally different from the continents”. ↩

    2. 10b.

      Page 1:  “The dramatic steepening of the hypsographic curve at mountains and oceanic trenches can only be maintained by a dynamic Earth. On geologic timescales, such features would quickly erode or fill in with sediments.” ↩

  11. 11.

    Dillow, Joseph C.  The Waters Above: Earth's Pre-Flood Vapor Canopy.  Chicago: Moody Press.  1981.  A 1981 book that describes a pre-Flood blanket of water vapour above the atmosphere, which condensed in forty days of rain.  The article uses it as the fullest statement of the canopy answer.

    1. 11a.

      Page 138:  Footnote 7.  “However, most of the water of the Deluge came from the fountains of the deep (Gen. 7:11).” ↩

  12. 12.

    Rush, David E., and Larry Vardiman.  “Pre-Flood Vapor Canopy Radiative Temperature Profiles.”  Proceedings of the Second International Conference on Creationism 2:231–246.  Creation Science Fellowship, Pittsburgh.  1990.  A computer calculation of how hot the surface would be under a pre-Flood canopy of water vapour, with no clouds and no convection (the rising and sinking of air).  Its authors worked at the Institute for Creation Research, and the paper includes the published discussion and the authors' closure.  It found that every canopy from 10 to 1013 millibars kept its water as vapour at the base, but canopies of 50 millibars and up made the surface inhospitably hot; the article uses it as the creationist calculation of that heat problem.

    1. 12a.

      Page 237:  “In conclusion, only 50 mb of water vapor added above the present atmosphere would raise the surface temperature as determined by a radiation balance from 320 K to 409 K.”  Page 236:  “50 mb of water vapor is equivalent to 20 inches of precipitable water.” ↩

    2. 12b.

      Page 245:  The authors' closure, answering the discussion.  “As Mr. Oard correctly notes, our 50 mb canopy (20 inches of precipitable water) would hardly provide 40 days and nights of heavy rainfall.” ↩

  13. 13.

    Vardiman, Larry, and Karen Bousselot.  “Sensitivity Studies on Vapor Canopy Temperature Profiles.”  Proceedings of the Fourth International Conference on Creationism, 607–618.  Creation Science Fellowship, Pittsburgh.  1998.  A test of how the 1990 canopy model responds when five settings it held fixed are changed, from about half to twice their normal values, for a canopy holding about 0.1 meters of water.  Halving the solar constant, the sun's output, cut the surface temperature from 335 K to 240 K, yet no change was dramatic enough to remove the problem of hot surfaces.  The abstract gives 2.0 meters as the most water such a canopy could hold, while the body gives 1.0 meter, quoted below; the article uses it as the canopy's own builders putting a price on the water.

    1. 13a.

      Page 616:  “If all five parameters were introduced into the model simultaneously such that the surface temperature was minimized, it is estimated that the water content of the canopy could possibly be raised to as much as 1.0 meter. This is less than 10% of the water content suggested by Dillow (1982). Unfortunately, this amount of water in a canopy would not contribute significantly to the waters of the Genesis Flood or produce significant pressure and density effects.” ↩

  14. 14.

    Vardiman, Larry.  “Temperature Profiles for an Optimized Water Vapor Canopy.”  Proceedings of the Fifth International Conference on Creationism, 29–40.  Creation Science Fellowship, Pittsburgh.  2003.  A 2003 conference paper by Larry Vardiman on the temperature profiles of an optimized water vapour canopy.  The article uses it for the finding quoted below, that all but the smallest modelled canopy were too hot to live under.

    1. 14a.

      Page 30:  “Canopies ranging in size from 10 to 1013 mb of water vapor (i.e., 10 cm to 1013 cm of precipitable water) were found to produce temperatures in radiational equilibrium at the canopy base hot enough to maintain water in the vapor phase. Unfortunately, except for the 10-mb (10 cm of precipitable water) canopy, all modeled canopies produced inhospitably high surface temperatures.” ↩

  15. 15.

    Sarfati, Jonathan et al.  “Arguments we think creationists should NOT use.”  Creation Ministries International.  Feb 7, 2006.  A living page from Creation Ministries International, a creationist ministry, that lists arguments creationists should drop and is revised as new evidence comes in.  It lists the vapour canopy among the arguments creationists should not use, and says some listed arguments are fallacious while others are merely doubtful.  The article uses it as a creationist ministry's own retreat from the canopy. ↩

  16. 16.

    Patterson, Roger.  “Did the Pre-Flood World Have a Vapor Canopy?”  Answers in Depth 21.  Answers in Genesis.  Mar 10, 2026.  An Answers in Genesis article by Roger Patterson that tells creationists to reject the vapour canopy as an outdated and flawed model.  The article uses it as evidence that a major creationist ministry now rejects the canopy.

    1. 16a.

      Patterson on Vardiman's 2003 paper:  “he argues that the only way to get a 'livable' temperature with a sizable canopy is to reduce the solar constant down to 25% of today's values. Previous models still gave temperatures in the hundreds of degrees even with as little as a meter of water—less than 10% of Dillow's suggested minimum. … The sun doesn't have a dimmer switch.” ↩

  17. 17.

    Austin, Steven A. et al.  “Catastrophic Plate Tectonics: A Global Flood Model of Earth History.”  Proceedings of the Third International Conference on Creationism, 609–622.  Creation Science Fellowship, Pittsburgh.  1994.  A 1994 conference paper by six creationist scientists that proposes a global Flood model of Earth history.  The article uses it for the claim that the fountains of the great deep are steam jets at the spreading ridges.

    1. 17a.

      Page 613:  “A second source suggested by [118,6,7] is condensing water from spreading center geysers. This should provide adequate water to explain up to 150 days of open 'windows of heaven'.”  On the canopy:  “This is insufficient water to contribute significantly to even forty days of rain.” ↩

  18. 18.

    Duncan, Hamilton.  “Volcanism, 'Fountains of the Great Deep,' and Forty Days of Rain.”  Creation Research Society Quarterly 47:9–19.  2010.  A geology paper by Hamilton Duncan, a professional engineer and geologist, in the summer 2010 issue, estimating the water that large igneous provinces (huge lava fields) could have released.  Its abstract says they could have supplied at least 58 cm of rain a day for forty days, but its own count for six provinces gives 4.4 cm, and its sampled water contents come out lower than earlier estimates.  The article uses it as the one attempt to price new water from below.

    1. 18a.

      Section Abstract, page 9:  “Gravimetric analysis of large igneous provinces indicates the liberation of water from their magmas could have contributed at least 58 cm of rain worldwide every day for forty days.”  Page 12:  “a volume of 605,603,000 km3 of basaltic magma would have yielded a total of 1.174 x 1023 grams H20. … yielding a total value of 1.190 x 1023 grams H20.” ↩

  19. 19.

    Computed for this article in research/yec-sources-and-sinks.md and the script budget2.py in scratch.  Duncan's 1.190 × 10²³ g of water is 1.190 × 10¹⁷ m³, which over 5.100 × 10¹⁴ m² is 233 m, or 583 cm/day for forty days, not 58.3; his mass figure is consistent with his own volume and water-content inputs, so the slip is in the final division.  Brown's V = 7.15 × 10²³ cm³ is 7.15 × 10⁸ km³, 1,402 m over the globe and 54 % of the 1.335 × 10⁹ km³ ocean; a smoothed earth with the chamber added stands 4.02 km deep, 4.8 km short of Everest.  Dillow's maximum canopy of 12.19 m is 0.47 % of the ocean; Vardiman's 1,013 mb canopy of 10.13 m is 0.39 %. ↩

  20. 20.

    Brown, Walt.  In the Beginning: Compelling Evidence for Creation and the Flood.  Distributed by Real Science Radio.  9th draft edition.  2019.  Walt Brown's book setting out the hydroplate theory, in which the Flood's water comes from a subterranean chamber.  The article uses it as the only model that states an explicit volume of water, and as the one that proposes a mechanism for the fifteen cubits.

    1. 20a.

      Page 600:  “V = 7.15 × 10²³ cm³”.  Page 601:  “about half the water in our oceans”. ↩

    2. 20b.

      Page 475:  “as the floodwaters rose and continents sank, this same buoyancy effect caused preflood mountains not yet covered by water to exert greater pressure on the water still under the crust. This reduced their height and lifted lower mountains, nearly equalizing mountain heights above the rising water—just as Genesis 7:20 states.” ↩

  21. 21.

    Mitchell, Elizabeth, and Andrew A. Snelling.  “Diamond with Ringwoodite Reveals Water Deep in Earth's Mantle.”  Answers in Depth.  Answers in Genesis.  Apr 17, 2014.  An Answers in Genesis article by Elizabeth Mitchell with Andrew Snelling on a diamond containing ringwoodite, a mineral from Earth's mantle, that reveals water deep in the mantle.  The article uses it for Snelling's reading of the find, quoted below.

    1. 21a.

      Section Fountains of the Great Deep:  “It confirms the capacity of the mantle to have housed the water that was released when the fountains of the great deep were broken up to commence the Flood, and the huge volume of water that was released through these fountains for as much as 150 days, providing more than enough water to help submerge the whole globe, just as described in Genesis 7:11–24.” ↩

  22. 22.

    Snelling, Andrew A.  Earth's Catastrophic Past: Geology, Creation and the Flood.  Institute for Creation Research, Dallas.  2009.  A two-volume book on geology, creation and the Flood, published by the Institute for Creation Research.  The article uses it for Snelling's account of how deep the Flood water stood over the pre-Flood mountains, and of how the pre-Flood land and sea may have been arranged.

    1. 22a.

      Page 473:  “the overall result of the Flood was that most of the Flood waters remained on the earth. Whether or not the volume of the ocean basins was greater after the Flood than before depends on the amount of new water added to the earth's surface. … This, in turn, implies three possibilities: either the proportion of land area to water area was larger before the Flood; the ocean basins were shallower before the Flood”. ↩

    2. 22b.

      Page 278:  “the Flood waters had covered all the pre-Flood hills and mountains right around the globe to a depth of at least '15 cubits' (approximately 22 feet or 7 meters).” ↩

  23. 23.

    Foley, Avery, and Troy Lacey.  “Where Did All the Floodwater Go?”  Answers in Genesis.  Apr 18, 2018.  A short web article from Answers in Genesis, a young-earth ministry, that answers the question where the Floodwater went.  The article uses it for the ministry's description of the pre-Flood earth, which gives the shape of the seas and mountains without a figure.

    1. 23a.

      Section Shallow Seas and Low Mountains:  “This pre-Flood world had shallower seas (no deep ocean trenches) and lower mountains, scattered across a single continent”. ↩

  24. 24.

    Baumgardner, John R.  “Numerical Simulation of the Large-Scale Tectonic Changes Accompanying the Flood.”  Proceedings of the First International Conference on Creationism 2:17–28.  Creation Science Fellowship, Pittsburgh.  1986.  A conference paper that reports a numerical simulation, a computer calculation, of the tectonic change its author attributes to the Flood.  Its abstract gives the sea-level rise as some 2,000 m, from replacing cold old ocean floor with hot, buoyant mantle material.  The article uses it for the sea-level mechanism that catastrophic plate tectonics offered, a mechanism its author later withdrew.

    1. 24a.

      Page 6:  “If we assume a temperature difference of 1000 K, a lithospheric thickness of 100 km, and a coefficient of thermal expansion of 2.5 × 10-5, we obtain an increase in the height of the ocean bottom as the old lithosphere is replaced of 2,500 m.” ↩

  25. 25.

    Clarey, Timothy L., and Davis J. Werner.  “A Progressive Global Flood Model Confirmed by Rock Data Across Five Continents.”  Proceedings of the Ninth International Conference on Creationism, 412–445.  Cedarville University.  2023.  A conference paper by two researchers at the Institute for Creation Research, based on nearly 3000 stratigraphic columns (the recorded sequences of rock layers) from oil wells, measured columns and seismic data across five continents.  It proposes that the Flood rose in stages and peaked near the end of the fifth of six packages of sedimentation.  The article uses it because it repeats the 2.0 km sea-level figure from Baumgardner's 1986 paper, a figure Baumgardner later withdrew.

    1. 25a.

      Page 439:  “Creationists have calculated that this elevated seafloor could have raised the global sea level by 1.6 kilometers (Snelling 2014c) to 2.0 kilometers (Baumgardner 1986), greatly helping flood the continents.” ↩

  26. 26.

    Walker, Tas.  “A Biblical Geologic Model.”  Proceedings of the Third International Conference on Creationism, 581–592.  Creation Science Fellowship, Pittsburgh.  1994.  A short paper that sets out a model of Biblical geologic history as a diagram and a set of named stages, and proposes that the model be tested against real geological sections.  It uses Ussher's chronology, which dates creation to 4000 BC and the Flood to 2300 BC.  The article uses it for the stage names that later creationist authors use for the rise and drainage of the Flood.

    1. 26a.

      Page 585:  “The first stage, during which the waters 'rose and increased greatly' until the whole earth was covered [Gen 7:18], has been called the Inundatory Stage. The second stage during which the waters receded from the earth [Gen 8:3,5] has been designated the Recessive Stage.” ↩

    2. 26b.

      Page 585:  “the 'springs of the great deep being closed' [Gen 8:2] is assumed to mean an intense world-wide disturbance which started the waters receding from the land and is called the Abative Action.” ↩

  27. 27.

    Pearson, D. G. et al.  “Hydrous mantle transition zone indicated by ringwoodite included within diamond.”  Nature 507:221–224.  2014.  A paper in Nature on a piece of the mineral ringwoodite trapped inside a diamond.  The authors say the water-rich inclusion is evidence that the mantle's transition zone holds water, at least locally, to about 1 weight per cent.  The article uses it as its direct evidence that the mantle holds water.

    1. 27a.

      Section Abstract:  “The water-rich nature of this inclusion, indicated by infrared absorption, along with the preservation of the ringwoodite, is direct evidence that, at least locally, the transition zone is hydrous, to about 1 weight per cent.” ↩

  28. 28.

    Ni, Huaiwei et al.  “Distribution, cycling and impact of water in the Earth's interior.”  National Science Review 4(6):879–891.  2017.  A paper in National Science Review on how water is distributed and cycled through the Earth's interior, and what it does there.  The article uses it for the claim that the mantle holds a large amount of water, and for the form that the water takes in the minerals.

    1. 28a.

      Section Introduction:  “Although not immediately evident, a huge amount of water, perhaps several times the mass of the entire hydrosphere, is stored in the Earth's interior.” ↩

    2. 28b.

      Section Abstract:  “nominally anhydrous minerals (NAMs) in the silicate Earth host a significant amount of water by accommodating H point defects in their crystal lattices.” ↩

  29. 29.

    Isaak, Mark.  “Problems with a Global Flood.”  TalkOrigins Archive.  2nd edition.  1998.  A hostile secondary source, an online FAQ last updated in November 1998, that tests what a literal Flood would require against what we actually observe.  The article uses it only for its framing, since every number in the article is taken from the primaries, the original sources it cites directly.

    1. 29a.

      Section Runaway subduction (subsection):  “Baumgardner estimates a release of 10^28 joules from the subduction process. This is more than enough to boil off all the oceans.” ↩

    2. 29b.

      Section New ocean basins (subsection):  “The water draining from the continents would have produced tremendous torrents. There is evidence of similar flooding in the Scablands of Washington state ... Why is such evidence not found worldwide?” ↩

  30. 30.

    Conrad, Clinton P.  “The solid Earth's influence on sea level.”  GSA Bulletin 125(7–8):1027–1052.  2013.  A research paper on how the solid Earth influences sea level.  The article uses it for the solid-Earth terms in the sea-level budget and for the water that slabs carry into the deep mantle.

    1. 30a.

      Section Abstract, page 1027:  “several such records indicate sea-level drop of ~230 m since a mid-Cretaceous highstand ... Most importantly, ridge volume decrease since the mid-Cretaceous, caused by an ~50% slowdown in seafloor spreading rate documented by tectonic reconstructions”.  The ridge term is at about 250 m, and the other terms of ~40, ~20 and ~60 m of fall are offset by about 60 m each from Atlantic sediment and dynamic topography. ↩

    2. 30b.

      Page 1045:  “van Keken et al. (2011) estimated, with admitted uncertainty, that slabs currently transfer ~3.2 x 10^8 Tg/m.y. of water into the deep mantle, which corresponds to roughly ~1 m/m.y. of eustatic sea-level drop if unbalanced by mantle degassing.” ↩

  31. 31.

    Stein, Carol A., and Seth Stein.  “A model for the global variation in oceanic depth and heat flow with lithospheric age.”  Nature 359:123–129.  1992.  A research article that fits one model to two sets of measurements, the depth of the ocean floor and the heat flowing out of it, at each age of the floor.  The model has a hotter, thinner lithosphere than previous models, the rigid outer layer of the Earth, and it fits the data better, including older floor that earlier models had treated as anomalous.  It describes a global average rather than any single ocean, and the article uses its figures for how deep new and old ocean floor lies.

    1. 31a.

      Page 125:  “GDH1 predicts an asymptotic depth for old lithosphere of 5,651 m, considerably shallower than the 6,400 m for PSM.”  GDH1 gives depth 2,600 + 365√t metres for floor younger than 20 million years. ↩

  32. 32.

    Seton, M. et al.  “A Global Data Set of Present-Day Oceanic Crustal Age and Seafloor Spreading Parameters.”  Geochemistry, Geophysics, Geosystems 21(10):e2020GC009214.  2020.  A technical data report that maps the age of the crust under today's ocean floor, using the magnetic stripes recorded on the seafloor and a model of how the plates moved.  It finds a mean age of 64.2 million years, slightly older than earlier estimates, and its own confidence grid marks the parts of the map that are least well constrained.  The article uses that mean age for how old the ocean floor is today.

    1. 32a.

      Section Abstract:  “the mean age of oceanic crust is 64.2 Myr, slightly older than previous estimates”. ↩

  33. 33.

    Miller, Kenneth G. et al.  “The Phanerozoic Record of Global Sea-Level Change.”  Science 310(5752):1293–1298.  2005.  A review in Science of how global sea level has changed over the past 543 million years, with a new record for the past 100 million years.  That record is built by backstripping, a method that removes the effects of sediment and sinking from the rock record, using five New Jersey coreholes.  It finds that sea level peaked at 100 ± 50 metres above today's during the Cretaceous, well below the 250 to 320 metres of earlier estimates.  The article sets that peak against the ceiling its ocean-floor model allows, to show what the record actually supports.

    1. 33a.

      Page 1294:  “we conclude that sea level in the Late Cretaceous was 100 ± 50 m higher than it is today.” ↩

  34. 34.

    Müller, R. Dietmar et al.  “Long-term sea-level fluctuations driven by ocean basin dynamics.”  Science 319(5868):1357–1362.  2008.  A paper in Science on long-term sea-level fluctuations, which its title ties to the dynamics of the ocean basins.  The article cites it in its passage on the tectonic lever, the idea that rising ocean floor pushed up the sea.

    1. 34a.

      Section Abstract:  “published estimates of the Late Cretaceous sea-level high differ by half an order of magnitude, from approximately 40 to approximately 250 meters above the present level.”  “we model a Late Cretaceous sea level that is 170 (85 to 270) meters higher than it is today.” ↩

  35. 35.

    Lambeck, Kurt et al.  “Sea level and global ice volumes from the Last Glacial Maximum to the Holocene.”  Proceedings of the National Academy of Sciences USA 111(43):15296–15303.  2014.  A research paper that fits a model to about 1,000 observations of past sea level from the last 35,000 years, taken far from the former ice sheets, to reconstruct how much ice the world held and how fast the sea rose.  It finds that the main melting ran from about 16.5 to 8.2 ka BP (thousands of years before present), and that the fastest rise, at least 40 millimetres a year, came at 14.5 to 14.0 ka BP.  The article uses that fastest rise and the paper's mantle viscosity values, the resistance of the rock to slow flow, to set what it calls the solid earth's speed limit.

    1. 35a.

      Section Abstract:  “the main phase of deglaciation occurred from ~16.5 ka BP to ~8.2 ka BP at an average rate of rise of 12 m⋅ka^-1 punctuated by periods of greater, particularly at 14.5-14.0 ka BP at ≥40 mm⋅y^-1 (MWP-1A)”. ↩

    2. 35b.

      Section Results:  Upper-mantle viscosity:  “the preferred minimum variance occurring at 1.5 x 10^20 Pa s [with 95% confidence limits of ~(1, 2) x 10^20 Pa s]”.  Lower-mantle solution:  “at 2 x 10^21 (7 x 10^20 - 4 x 10^21) Pa s”.  Or:  “~7 x 10^22 (1 x 10^22 - 2 x 10^23) Pa s”. ↩