Ocean Planets, Land to Ocean Ratio, and a Self-Arrest Mechanism in Waterworlds

by Dr. Tahir Yaqoob on August 15, 2012

An extremely interesting preprint of a paper appeared on arXiv in early August 2012 that comes to some fascinating theoretical conclusions about the habitability and time-evolution of waterworlds, or ocean planets. The paper is entitled Indication of insensitivity of planetary weathering behavior and habitable zone to surface land fraction, by Abbot, Cowan, and Cielsa.

Waterworlds, or ocean planets have no counterpart in our solar system. None have actually been found outside our solar system either, so they are at the moment just theoretical possibilities. The concept covers planets that could have a range in depth of a complete ocean covering, possibly even up to hundreds of kilometers. The latter is perhaps the most intriguing- imagine intelligent life-forms having developed in such a world; networks of cities, metropolises, “aquaparks,” and “highways,” stretching out in all three dimensions in a liquid abyss. Sports would be very different. But we digress.

There are several things that stand out about the Abbot et al. paper that I like. There is the approach to the problem, and then the honesty about what can be achieved and frank discussions about robustness (or otherwise) of the results, with no attempts to claim things on a flimsy basis. The general problem of modeling a planet’s climate is so immensely complex that we don’t even know how to do it properly for Earth because of, amongst other things, unknown critical quantities. The modern approach is often to throw complex computer codes and simulations at the problem and then try to make sense of the stuff that comes out. This is often accompanied by the frustrating task of figuring out whether some of the results are actually due to artifacts of the numerical number crunching with finite precision, or whether they are real. (The problem of stuff falling into a black hole via a disk is notorious for this sort of thing: phenomena appear in the results that can be entirely fictitious. People are still working on understanding these accretion disks after many decades.)

With the enormous increase in computing power in the last three decades it has become too easy to kiss goodbye to simple insights by treating a problem with numerical code. The approach of Abbot et al. is therefore refreshing with no computer simulations at all, but is simply to see what can be learned “by hand.” The problem is boiled down to a skeleton framework, a few simple assumptions are made, and then the conclusions are tested for robustness to those assumptions and simplifications. The conclusions are new with respect to the effect of the land to ocean ratio of a planet on certain aspects of its habitability.

The actual paper is actually quite long and heavy-going and the introduction alone is more than two journal pages which in itself is unusual. A solid background to the problem and a clear description of the adopted approach is given in the introduction. The goal is simply put: “The main objective of this paper is to investigate the effect of land fraction on the carbon cycle and weathering behavior of a terrestrial planet in the habitable zone.” What is referred to here is one of the key factors that determines habitability in the traditional sense: the silicate compounds on a terrestrial planet react with carbon dioxide in the atmosphere (weathering) to produce carbonates and silicon dioxide. The whole cycle is extremely complex and is affected by biology. If the carbonates are eventually buried in ocean sediment, the net carbon dioxide can go down but then biological precipitation can increase the carbonates in the ocean. Carbon lost to Earth’s mantle can appear again by volcanic outgassing (in the form of carbon dioxide). So, how can such a formidable problem be made tractable (with or without the fancy code)? To quote from the introduction of the paper again:

“We will outline and use a simple analytical model for weathering and global climate that necessarily makes grave approximations to the real physical processes. For example, we will use existing parameterizations of seafloor weathering, while acknowledging that observational and experimental constraints on such parameterizations are minimal. We will only use the model, however, to make statements that do not depend strongly on uncertain aspects of the parameterizations. This model should be used to understand intuitively the qualitative behavior of the system rather than to make quantitative estimates.”

One condition that is imposed on the scope of the investigation is that it is restricted to planets with a water fraction by mass (of the total planet, not just the land), of 10 times the water mass fraction of the Earth. The latter is stated as 0.02&#37 to 0.1&#37, so presumably this means including planets with a water mass fraction of up to 1%. The authors state that waterworlds with more like 10% water or higher will have vastly different physics operating so are not considered here. The investigation considers land to ocean (area) covering factors ranging from 1% (the authors state the latter is equivalent to Greenland plus Mexico) to 99% (the number for Earth is stated as 30%). Covering factors of zero (i.e. pure ocean, no land above sea level at all) are also considered.

In order to avoid this post becoming too long and tedious, I will now go straight to the conclusions. A major finding is that varying the land fraction between 1% and 99% has very little effect on climate, it being insensitive to even external forcing in the face of a broad range of illumination. Yet a land fraction of zero “causes a huge shift in planetary weathering behavior.” In other words, even a tiny bit of land, a small continent, is sufficient to fire up a weathering-climate feedback, and turning the land fraction up to 99% makes little difference. But if you get rid of the land completely, the feedback mechanism is gone and the resulting behavior is completely different. In assessing the robustness of the result, the authors state that the current best estimate of seafloor weathering on modern Earth would have to be wrong by a factor of 2 to 3 in order for the main conclusion to be invalid. And of course we are reminded of how fine-tuned Earth is in yet another way: if the oceans were a few times deeper than they are, Earth would be a waterworld. An Earth without legs! No animals with legs would have been necessary (yes that means us too).

Some other caveats are discussed about the robustness of the main conclusion and it is probably fair to say that there is a sufficient range of conditions for validity that the result is interesting enough to pursue with more detailed investigations and also serves as an important framework in which to assess interpretations of future observational data. However, one of the implications is that it will be observationally difficult to actually measure the land fraction on exoplanets, which is just the flip side of the result of insensitivity to it. The reason why it might be important to measure the land fraction is that it affects the width of the habitable zone and a non-zero land fraction is suggestive of enabling long periods of stable climate. The authors explain that it may be possible to estimate the land fraction with future missions but curiously talk about the Terrestrial Planet Finder mission, which was cancelled in 2007. Anyway, it is pointed out that the exoplanet should be “not much cloudier than Earth” (if the land fraction is to be probed). I guess that means we won’t be finding any more exo-Londons too soon (I grew up in the exo-London on this planet).

Going back to the pure waterworlds, we see that an implication of the results of the Abbot et al. study is that they will have narrower habitable zones than planets with land. Another conclusion is that if it is true that seabed weathering does not depend on the surface temperature of the planet, seabed weathering could proceed fast enough to deplete carbon dioxide quickly enough to start exposing land if the oceans were not too deep. The result of this would be to slow down the process as soon as even a little bit of a land is exposed, thus completely changing the physics operating. The authors call this “self-arrest” of a waterworld. An interesting implication is of course that it is possible that the Earth itself went through this self-arrest phase after starting out as a waterworld. The self-arrest idea is, in the words of the authors, “profound, because it implies that waterworlds that form in the habitable zone have a pathway to evolve into a planet with partial ocean coverage that is more resistant to changes in stellar luminosity.”

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