Where is the water on Venus?

Given that Venus has the same CO2  budget as the Earth, and approximately the same nitrogen budget as the Earth (to within a factor of 3), and under the assumption that carbon dioxide, nitrogen and water were all delivered to the young Earth and Venus by comets, Venus should have approximately as much water as does the Earth.  Yet Venus is bone dry.

Deuterium: the missing link

Remember that elements can have several different isotopes. The properties of atoms are determined by the numbers of protons and electrons they have, not by the number of neutrons. Normally,  hydrogen has 1p + 1e. Deuterium is hydrogen with one neutron added to the nucleus. Tritium is hydrogen with two neutrons. All three behave as normal hydrogen but deuterium and tritium are more massive, or heavier,
isotopes of hydrogen.

Water, we all know, is made of two hydrogen atoms and one oxygen atom,  H2O. However, we could make heavy water using deuterium or tritium. We could write one of these as HDO. Nature has seen fit to make about one in every 10,000 hydrogen atoms deuterium. Since each water molecule has two hydrogen isotopes, one in every 5,000 water molecules should have a deuterium atom. For some perspective, it is important to note that all materials on Earth with hydrogen have the same ratio of dueterium to hydrogen (D/H); in addition, moon rocks, all meteorites and comets have the same D/H ratio as that of Earth. And as best as we can tell, the D/H ratio also is the same in the atmospheres of the giant planets, in the Sun, in the material between the stars, everywhere. This is because all the D and H in the universe formed in the first moments of  the Big Bang.  While all other elements are created in stars through nuclear fusiion, no new D or H has been created since the beginning of the universe.

Deuterium and Venus

The Pioneer Venus spacecraft included probes that parachuted through the atmosphere to measure the gases, temperatures and pressures in the atmosphere. One of the unusual results found is that the D/H ratio on Venus is 100 times larger
than that found on Earth (or moon rocks, or anywhere else in the solar system).  Venus is very unusual. Why? It is highly unlikely that Venus started out with an odd D/H ratio, so let's assume that it began normally and something happened that changed that ratio.  What happened?

Imagine that Venus once had a D/H ratio identical to that of Earth.  But since H is lighter than D, it is more likely to escape from Venus.  Thus, if atmospheric escape of H and D can occur at a rate slow enough that it is easy for H to escape but fairly hard for D to escape, the D/H ratio would slowly increase as H escaped faster than D.

The escape velocity from Venus is 10.4 km/sec. The thermal velocities for H and D at temperatures appropriate for Venus are 5 and 3.5 km/sec. So, since 10.4 km/sec is barely twice and thrice these thermal velocities for H and D, and much less than our factor of six rule of thumb, we conclude that both species can escape but that H can escape much more
easily.   Contributing to the escape of H and D is the lack of a magnetic field for Venus.  Unlike Earth, Venus has no magnetic field, probably because its slighly lower mass prevents it from having a solid inner core, and it is the continuing freezing of liquid iron from the outer core onto the inner core that generates energy (heat is removed from something when it goes from liquid to solid) that drives the geodynamo that generates our magnetic field).  And the lack of a magnetic field means that Venus has no protection from the solar wind, so the solar wind can strip atoms from the top of Venus' atmosphere.

How much would have to escape to change the D/H ratio from 1/10,000 to 1/100? If we started with

Dinitial = 100
Hinitial = 100*10,000=1,000,000
and we finished with
Dfinal = 10
Hfinal = 1,000
we would change from
(D/H)initial = 1/10,000
(D/H)final = 1/100.
In this case, we would lose 90% (90 out of 100 atoms) of D and 99.9% of the H (999,000 out of 1 million).   Thus, we can end up with this high D/H ratio if Venus had an abundance of hydrogen in it's atmosphere such that preferential mass loss could occur and lost 99.9% of it's hydrogen.

But where do the hydrogen isotopes come from? The terrestrial planets do not have free hydrogen molecules or atoms in their atmospheres and most  likely never did. Rocks on terrestrial planets do not contain hydrogen unless the hydrogen was derived from water.  Of the gases or volatiles in the terrestrial planets atmospheres and hydrospheres, only methane (CH4), ammonia (NH3) and water (H2O) contain hydrogen. Since methane and ammonia are not abundant it is likely that water is the principal reservoir for hydrogen.

Thus, we are led to conclude that Venus lost at least 99.9% of the water it started out with.

Now we imagine that Venus once had oceans and water vapor in the atmosphere.  Perhaps Venus was had an Earthlike environment, but without life:

Why might this have happened on Venus?

It might have happened very gradually.  Image Venus a long time back. The planet is nearly identical in size, mass, composition and distance from the Sun as the Earth. It begins like the Earth with global oceans, with CO2 dissolved in the oceans, with carbonate rocks forming at the bottoms of the oceans. Heat from the interior drives plate tectonics and volcanic activity, recycling carbon from the rocks to the atmosphere.

But because Venus is just a tiny bit smaller than the earth (81.5% of the Earth's mass), it has less radioactive heat sources inside. Thus, at some time in the distant past, perhaps only 500 million -1 billion years ago, Venus may have ran out of enough internal heat to continue to drive the tectonic activity.

Alternatively,  because Venus is a little closer to the Sun, we would expect that the original temperature of Venus should have been a little warmer than that of the early Earth (although the feedback effects  --

hotter -->
more clouds -->
higher levels of reflected sunlight back to space (higher albedo) -->
lower levels of absorbed sunlight -->
lower temperature ?
-- make this hard to estimate. The slighly elevated temperatures puts a bit more water in the oceans and atmosphere and a bit less in the rocks. This makes the rocks harder since water serves as a lubricant for the plate tectonic process.

Either way, tectonic activity begins to slow down. The higher temperature drives more water into the atmosphere. The added water vapor pressure drives more CO2 out of the oceans and into the atmosphere. The added H2O and CO2 in the atmosphere increase the greenhouse effect. The higher temperature evaporates more water driving more H2O and CO2 into the atmosphere. The process "runs away."

The CO2 has nowhere to go since neither C nor O can escape; but solar UV breaks up the H2O and the H can escape, leaving behind the O.

How was Venus Different From Earth, 4.5 BY ago?

Early in the history of Venus and Earth, perhaps soon after the great bombardment, we can easily imagine both planets settling down to be comfortable, wet planets of similar size and location in the solar system.  No other two planets in the solar system would appear to be more alike.  And yet Venus and Earth are now incredibly different.  Perhaps, then, the similarities are impressive but the small differences are far more important.

With this in mind, we can identify three fundamental differences between Venus and Earth that might have made all the difference in how the two planets' histories diverged.

  1. Life formed (somehow) on Earth.  Ultimately, this led to the production of oxygen and an ozone layer, thereby protecting the surface from ultraviolet light.
  2. Venus is a tiny bit closer to the Sun than is Earth. Consequently, Venus receives more sunlight per unit area of the surface.  (see next section).
  3. Venus' mass is only about 80% of Earth's mass.  Consequently, Venus has no magnetic field.  Why? Remember that the Earth has three distinct internal layers: the crust, the mantle, and the iron core.  But the core actually has two layers, a solid inner core and a liquid outer core.  The mass of the Earth is such that the pressure (due to Earth's own gravity) at the center of the Earth is high enough to squeeze iron and force it to undergo a phase change from liquid to solid (note that a phase change, e.g., liquid water to ice, occurs due to a decrease in temperature or an increase in pressure).  Consequently, the inner core of Earth continues to grow as material from the outer core is continually deposited on solid inner core at the inner-outer core boundary.   Now, when a material undergoes a phase transition from liquid to solid, heat is released.  We all know this well in dealing with ice cubes - you must remove heat from water to make ice and, conversely, you must add heat to ice to melt the ice.  Thus, heat is released at the base of the outer core.  When a liquid is heated from below, the hot liquid will rise, thereby establishing a convection cell.  In the outer core, we end up with convecting liquid iron.  This moving iron generates a magnetic field and this process is called the geodynamo.  Venus has almost the same mass as Earth, but the 20% difference is just enough to prevent the solidication of an inner core in Venus.  Without a magnetic field, a planet's atmosphere is subject to the sandblasting effect of the solar wind.

The Greenhouse Effect

Again, we imagine a Venus that is Earthlike with respect to it's climate.  All other things being equal, Venus is closer to the Sun than the Earth, at 0.723 AU vs. 1.000 AU.  Thus, Venus gets

times more sunlight than does the Earth, since the amount of light received is inversely proportional to the square of the distance from the light source.

Again, all other things being equal, the temperature of an object increases in proportion to the fourth root of the amount of energy received (this is called the Stephan-Boltzman law). Thus,

TVenus = (1.9)1/4 TEarth = 1.17 TEarth
where TVenus is the temperature of Venus and TEarth is the temperature of Earth.    From basic physics, we know that TEarth = 253 K (-20 C = -4 F) if the only factor controlling the temperature were the amount of sunlight received by the ground on the Earth. Thus, we find from these very simple considerations and some fundamental laws of physics (the inverse square law for light; the Stephan-Boltzman law for temperature) that
TVenus= 297 K (24 C = 75 F).
Yet, we know that the temperature of Venus is 737 K (464 C = 867 F)!    This is the consequence of the greenhouse effect.

Let's look at what really happens to sunlight when it reaches Earth.

This amount, 33%, is called the albedo of Earth, the total amount of incident sunlight that simply bounces off Earth and does not contribute at all to heating the atmosphere. Thus, a total of 45% of the incident sunlight ultimately reaches the surface and is absorbed by rocks and the oceans.

Now, let's look at what happens to the light absorbed by the ground.

The ground cleary must warm up.  Warm things radiate heat to cool off, so the ground gives energy in the form of infrared light.  We associate infrared light with "heat" because water molecules are excellent devices for absorbing infrared light.  Thus, a "heat lamp" is red because most of the light it produces is in the infrared.

Water is not the only good molecule for absorbing infrared light.  Carbon dioxide is also an excellent absorber.  Between the H2O and CO2 nearly all the upward going infrared light is absorbed in the atmosphere. In effect, this means atmosphere gets heated by the original  22% plus an additional 45%, for a total of 67%.

Now we have to think about the atmosphere.  It also is heated up, both by sunlight from above and infrared light from below. Thus, the atmosphere has to give off heat.   The atmosphere is not biased so it emits infrared light in all directions; effectively, half goes up and half goes down.

Therefore, the ground is now receiving more heat than the original 45% because some of the light is sent back down to the ground a second and third and fourth time! The net effect ultimately is that the ground effectively abosrbs 77% of the amount of sunlight that hits Earth, even though 33% is reflected off into space!

This has the effect of increasing the amount of energy absorbed by the ground by 71% (from 45 to 77 units of energy).  Again, using the Stephan-Boltzman law, we find that the temperature of Earth should increase by

TGreenhouse Earth = (1.71)1/4 TEarth= 289 K (16 C = 61 F)
so the temperature of Earth is increased by 36 K (36 C = 65 F) because of the Greenhouse Effect.

On Venus, the atmosphere is so dense with CO2 that light goes up and down and up and down, effectively heating the ground many times over so that the temperature goes from 297 K to 737 K!  Thus, the Greenhouse Effect increases the surface temperature on Venus by 440 K.  This is one hell of a runaway greenhouse!

How did this happen?  Let's revisit our scenario from above.  In an Earthlike environment, but without life: