FeSiOss CO2g FeCO3s SiO2s

In all of these reactions, the carbon in gaseous CO2 exchanges with the silicon in solid silicate minerals, to form a solid carbonate mineral plus solid silica (SiO2, of which quartz is one form, and which is also common in beach sand). The reader should keep in mind that the actual silicate minerals involved in the formation of carbonates can be considerably more complex than the simple chemical compounds referred to in the above reactions, and may have different equilibrium and kinetic properties. The feldspar family of minerals is one of the most important players in silicate weathering in Earth's present crust. These minerals are aluminum silicates involving varying amounts of sodium, potassium, and calcium; their weathering products include a broad variety of clay minerals, rather than just simple silica. Nonetheless, the Ebelmen-Urey reactions are often taken as indicative of what is going on in more realistic cases.

First, let's take a look at the equilibria that would be reached in the Ebelmen-Urey reactions after a sufficiently long time has passed. Imagine, for example, putting a pile of powdered MgSiO3 in a closed chamber filled with a large quantity of CO2 gas, and holding the entire apparatus at constant temperature T. The gas will react with the silicate to form carbonate and silica, drawing down the pressure until the products have built up to the point that the rate of recombination of

Figure 8.1: Equilibrium CO2 partial pressure as a function of temperature for equilibrium with magnesium (Mg), iron (Fe) and calcium (Ca) silicates.

Temperature (K)

Figure 8.1: Equilibrium CO2 partial pressure as a function of temperature for equilibrium with magnesium (Mg), iron (Fe) and calcium (Ca) silicates.

carbonate plus silica is equal to the rate of reaction of CO2 with silicate, at which point equilibrium has been reached. As long as the silicate has not been used up, the pressure will equilibrate at a value that depends only on T. Since the activities of the solid phases in Eq. 8.7 are unity, the only activity that can vary is that of the gaseous CO2, and this activity can be characterized by the partial pressure of the gas. As long as none of the solid reactants has been exhausted, chemical equilibrium for any one of the reactions in Eq. 8.7 is described entirely in terms of the way the partial pressure of CO2 gas (pCO2 in chemical parlance) depends on temperature, when in the presence of the three solid reactants in the equation. In this situation, when there is only one activity which can vary, the equilibrium constant can be taken to be pCO2 itself, and its temperature dependence follows the Arrhenius law

where pi is some constant, R* is the universal gas constant and AH is a characteristic energy, specifically the difference in enthalpy of formation between the products and reactants. For the Ebelmen-Urey reactions, the reaction releases energy (i.e. is exothermic), so AH is positive. If the gas constant R* is given in J/Mole ■ K then AH has units of J/Mole. The equation for partial pressure looks just like the Clausius-Clapeyron relation, and this is no accident since the thermodynamic formalism for the temperature dependence of equilibrium pressure is identical in the two cases: formation of a condensed phase from a gas is just a form of chemical reaction involving a single substance. The latent heat of fusion for water is 158 kJ/Mole, which compares with AH values of 79496, 88700 and 64852 kJ/Mole for the Mg, Ca and Fe reactions measured in the laboratory at 298K.

The equilibrium pressures for the three reactions are shown as a function of temperature in Fig. 8.1. The measured temperature dependence of AH has been taken into account in calculating these pressures. First, we note that at Earthlike temperatures the equilibrium partial pressures for Mg and Ca minerals are very low. For the Mg case at 300K the equilibrium has pCO2 _ 1.9 • 10_5bar, or equivalently 19 ppmv in a 1 bar background atmosphere. For the Ca case, it's even lower, amounting to a mere 0.1 ppmv. In equilibrium, weathering of Mg and Ca silicates would draw down atmospheric CO2 to such low values that it would have little greenhouse effect. At present (and probably for most of Earth history), the pCO2 is well in excess of these equilibrium values, so silicate weathering is always trying to reduce atmospheric CO2 to nearly zero, though it never gets especially close to equilibrium because the system is kept out of equilibrium by outgassing of CO2 from the interior. Weathering of iron silicates leads to a somewhat different story line. At 300K the equilibrium for the Fe case is 0.006 bar, or 6000 ppmv. This is well in excess of the present pCO2, and probably in excess of any value attained in the past half billion years. The implication is that even if iron silicates were prevalent at the surface of the Earth, the weathering of Mg and Ca silicates keeps the atmospheric CO2 too low for iron carbonates to form. On the other hand, we know that during the era of the Faint Young Sun the CO2 must have been well in excess of 0.006 bar if the CO2 greenhouse effect is to be strong enough to keep the Earth unfrozen. Under these circumstances, iron carbonates should have formed. Therefore, the presence of iron carbonates in ancient deposits serves as a proxy for high CO2. The lack of iron carbonates in certain Archaean formations is often taken as evidence that CO2 alone could not have been the answer to the Faint Young Sun paradox, but this interpretation should be treated with caution, since so little Archean surface rock is preserved and the temporal record is very sporadic.

The equilibrium pressures rise sharply with temperature At 700K the equilibria are 1200 bars, 45 bars and 15000 bars for the Mg, Ca and Fe cases, respectively. Because the Earth's interior temperature exceeds 700K not too far below the surface, this immediately implies that as carbonates and silica are engulfed by plate tectonics and subducted into the interior, CO2 will be cooked out of the rocks and outgas through volcanoes and fissures, allowing the carbon to be returned to the atmosphere. Things are likely to work similarly for any planet with plate tectonics and a rocky crust, and there may be other (as-yet unknown) means of episodically engulfing crustal material and bringing it to a high enough temperature to release CO2. The high-temperature equilibria also have implications for the state of the atmosphere and crust of Venus. The atmospheric surface pressure of Venus is about 90 bars of nearly pure CO2; this is well below the equilibrium pressures for Mg and Fe carbonates, so these minerals would be unstable at the surface of Venus, given sufficient S«O2. In contrast, the equilibrium pressure for Ca carbonates reaches 90 bars at 737K, which is quite close to the actual surface temperature of Venus. It thus appears possible that the atmosphere of Venus is in equilibrium with a crustal reservoir of calcium carbonate.

There are no atmosphere-bearing planets in the Solar system at present with surface temperatures intermediate between those of Earth and Venus, Venus may have experienced such temperatures in the past in the course of a near-runaway greenhouse state, and extrasolar planets could well have an orbit and composition to put them in this range. At 400K the Ca equilibrium is still only 650 ppmv, though that for the Mg case amounts to 5% of a 1 bar atmosphere. By the time one gets to 500K, however, large amounts of CO2 are inevitably left in the atmosphere - 6 bars for the Mg case and 0.12 bar for Ca case. Reasoning by analogy from the state of the present Earth atmosphere, when the system is out of equilibrium by virtue of outgassing from the interior, the actual atmospheric pCO2 will be considerably in excess of the equilibrium value, though it is reasonable to conjecture that at high temperatures equilibrium might be approached more rapidly, which would allow the system to stay closer to equilibrium even in the presence of substantial outgassing.

The chemical equilibrium behavior of the silicate/carbonate/CO2 system is straightforward, but it is probably the only thing that is straightforward about silicate weathering and its role in climate evolution. The picture of the CO2 in an atmosphere as being in equilibrium with rocks near the surface may perhaps be valid for some planets with a high temperature surface, but in general it is a poor representation of what is going on. Certainly, this is the case for Earth, the atmosphere of which is far out of equilibrium with the surface. The inorganic carbon cycle on Earth and probably many other rocky planets with an Earthlike temperature is a dynamic equilibrium which involves both interior and crustal processes. The carbonates near the surface are engulfed in subduction zones and brought into the interior of the planet, where the temperature is high enough that equilibrium is reached quickly and CO2 is driven almost entirely out of the carbonates. This CO2 outgases through volcanoes and through submarine features like the mid-ocean ridge where new ocean crust is born. If no new carbonates were formed by reaction with silicates, atmospheric CO2 on Earth would build up to very high levels. Current CO2 outgassing rates have been estimated at

0.1gigatonnes of carbon per year, or about 2 ■ 10-4kg/m2 of carbon. In 4 billion years this would pump 784,215 kg/m2 of C into the atmosphere, which is equivalent to a CO2 surface pressure of over 280 bars - about a million times the amount observed in the atmosphere today. Since it is extremely unlikely that the outgassing rate was much lower in the past ages - indeed it was probably greater when the Earth was younger and had lost less interior heat - there clearly must be an effective removal mechanism which takes CO2 out of the atmosphere. Formation of carbonates by reaction with silicates is by far the most likely candidate.

Rather than building up until the supply of interior carbon is exhausted, the atmospheric CO2 only builds up to the point where the rate of formation of carbonates equals the rate of outgassing. For any given outgassing rate, then, determination of the amount of CO2 in the atmosphere requires that we quantify the way the carbonate formation rate depends on CO2 levels, temperature, and other aspects of the climate. This is unfortunately not a matter of simple chemistry. For low temperature planets like Earth the carbon dioxide pressure at the surface is generally well in excess of the equilibrium value corresponding to surface temperature and composition, but the rate at which carbonates form and bring the system back toward equilibrium is not determined primarily by the kinetics of the chemical reaction. The quantity we need to understand is the weathering rate W which is the number of Moles of CO2 per unit time which is converted to carbonate by reactions with silicates over the entire surface of the planet. We need to determine how W depends on temperature, precipitation, and other aspects of climate, as well as the nature of the surface of the planet we seek to understand.

As with so many facets of planetary climate, silicate weathering involves a conspiracy of CO2 and water, and this is of central importance in the determination of weathering rates. Although the reactions as written in Eq 8.7 do not involve water, at Earthlike temperatures the reactions occur in solution when water comes into contact with rock, and should be thought of as a kind of dissolution of silicate minerals in the presence of the weak carbonic acid formed when CO2 dissolves in liquid water. At low temperatures - certainly below 300K and perhaps below 400K - the dry reaction proceeds too slowly to be of significance over a time scale of a few billion years

1. Given that the reaction is aqueous, it would be natural for the reader to conclude that silicate weathering on Earth would be dominated by undersea processes; after all, there is plenty of water there as well as plenty of silicate in the ocean floor. Contrary to expectations, however, the best estimates indicate that at present seafloor weathering amounts to only a tenth of the global total. The factors limiting seafloor weathering at present include the degree of acidity of the ocean, the low deep ocean temperatures, the composition of the ocean crust and the sluggish delivery of ocean

1The kinetics of the dry phase reaction do not appear to have been quantified to any great degree. There is some laboratory evidence that CO2 can be formed in dry reactions between carbonate and silica at temperatures above 500K, and indeed the dry phase reaction must be taking place in Earth's interior to sustain outgassing. It is generally believed, though, that even at high temperatures carbonates cannot form at a significant rate without water.

water to new reactable surfaces (occurring primarily in hydrothermal systems today). One should not over-generalize from this state of affairs, since it is highly dependent on the current state of the climate, and in a radically different climate with much higher CO2 and higher temperatures things could be quite different. Further, on Snowball Earth or on a waterworld with no crust exposed to the atmosphere, seafloor weathering would be dominant because it is the only form of weathering there is. Moreover, it is quite difficult to estimate the rate of seafloor weathering even in present conditions, and there are credible estimates suggesting that seafloor weathering accounts for a considerably higher proportion of the total than the standard picture would indicate. If seafloor weathering were to prove to be a considerable fraction of the total, then most of what we shall have to say subsequently about silicate weathering and climate regulation would be called into question. Climate evolution under the dominant control of seafloor weathering represents largely unexplored territory.

We shall adopt the conventional picture that silicate weathering for planets in a regime something like that of the Earth occurs primarily over land, as a result of rain washing over silicate bearing rocks. As a result, the rate of carbonate formation is expected to increase with the rate at which rain falls over weatherable silicate rocks; the rain both accelerates the reaction and carries away the soluble carbonates, exposing fresh silicate for further reactions. The functional form of this relation cannot be measured in the laboratory, and depends on the mineral, its physical structure and the presence of vegetation and other biological activity. There have been numerous attempts to estimate the precipitation dependence from various kinds of field measurements of weathering, but the process is still poorly constrained.

Laboratory measurements of aqueous phase silicate weathering show clearly that the rate of carbonate formation increases with temperature according to the Arrhenius law, exp(-E/R*T), where E is an empirically determined activation energy. When the range of temperatures about some base temperature To is not too large, the Arrhenius law can be simplified to the exponential form W(To) exp((T - To)/TU), where Tu = T^R*/E. The coefficient Tu varies amongst minerals and also depends on other conditions such as the acidity of the environment in which weathering occurs. Typical values in widespread use in weathering models lie in the vicinity of 10 K, for temperatures within a few tens of degrees of Earth's current surface temperature. It is generally assumed that the temperature-dependent reaction rates measured in the laboratory lead to the same temperature dependence of net weathering rate in the field, though it is far from clear that this should be the case. If rain remains in contact with weatherable rock for only a short time, then it would be expected that increasing the reaction rate would indeed increase the amount of carbonate formed; this is the prevailing view of what is going on in Nature. However, in circumstances where water remains in contact long enough for the reaction to come to equlibrium, the kinetics becomes irrelevant and the weathering rate should not be directly dependent on temperature, though it will still depend indirectly on temperature through the effect of temperature on the precipitation rate. Because of the steep exponential dependence of the reaction rate, the chemical kinetic effect is likely to become far less important as temperatures become much hotter than that of the present Earth. For example, with Tu = 10K, a reaction that takes one day to reach equilibrium at 300K would equilibrate in only 4 seconds at 400K and 178 microseconds at 500K. Given the slow kinetics at Earthlike temperatures and below, it does seem a reasonable assumption that something like the Arrhenius law applies for such temperatures. For very hot conditions, as in a near runaway, the direct temperature dependence of W would need to be reconsidered, however.

A more problematic issue is whether W also depends directly on the partial pressure of CO2 in the atmosphere. Note that this is a separate question from the indirect effect of CO2 concentration on weathering, mediated by its effect on temperature and by the effect of temperature on precipitation. Normally, for gas-solid reactions, it would be expected that the reaction would proceed more rapidly if there were more molecules of the reactive gas around. This is precisely what happens in laboratory measurements of the weathering of specific silicate minerals (mostly feldspar) at temperatures of 400K or more. The directly measured high-temperature dependence is often extrapolated down to lower temperatures using the Arrhenius law. However, laboratory measurements at Earthlike temperatures, conducted in the presence of organic acids thought to be similar to those produced by land plants, very clearly show that weathering rate is essentially independent of the amount of CO2; such experiments have been conducted for CO2 partial pressures ranging from about 0.3mb all the way up to 1 bar. The prevailing view in this subject seems to be that without land plants (or perhaps, without bacterial life modifying silicate surfaces) there is a power law dependence of weathering rate on CO2 partial pressure, but that this dependence disappears once land plants have appeared on the scene. It is quite unclear whether lichens or bacterial life are sufficient to cause the transition in behavior, and it is even more unclear whether the supposed abiotic pCO2 dependence really exists at low temperatures. One can also wonder whether abiotically produced acids could also eliminate the direct pCO2 dependence

The weathering rate is affected by a number of other processes going on at the surface. Notably, once land plants are on the scene, changes in precipitation and temperature distributions will affect the distribution of land plant cover, and this will feed back on the weathering rate; this is a very difficult feedback to model. Besides, that, the weathering rate depends on the availability of weatherable surface area. This is affected by physical erosion rates, and can be greatly enhanced by mountain-building such as the rapid uplift of the Himalayas; erosion rates are also affected by glacier flow and by freeze-thaw cycles which can fracture rock. Volcanism is also important in providing fresh weatherable surfaces. On Venus today, weathering is likely to be slow even for reactions that can take place without liquid water, because most of the erosional processes that produce fresh weatherable surface are absent or weak.

Note also that the conventional picture of silicate weathering on relatively cool planets like the present Earth presumes that the equilibrium atmospheric CO2 is far below the prevailing atmospheric value, so that the weathering can be thought of essentially driving the atmospheric CO2 towards zero. If, in contrast, the equilibrium has a significant amount of CO2 left in the atmosphere, then one needs to take into account the actual equilibrium toward which the weathering reactions are driving the system. This becomes more and more of a significant factor as the temperature increases, and the importance of the effect also varies with the surface mineralogy, since the equilibria are dependant on what kinds of reactions are taking place. The following development adopts the conventional cool-planet formulation in which weathering reactions are slow enough relative to outgassing rates that the atmospheric CO2 is always far above the equilibrium value.

Suppose that we have somehow managed to write the weathering rate as a function W(P, T,pCO2), where P is the rate at which precipitation falls over land. Then, if r is the outgassing rate, measured in the same units as W, equilibrium is determined by W(P,T,pCO2) = r. r may change gradually over geological time, leading to long term changes in climate. The problem is then closed if CO2 is the dominant greenhouse gas controlling climate, since then T and P can be determined as functions of CO2,given other pertinent data such as the solar (or stellar) constant at the planet's orbit and the configuration of the continents. Continental configuration can strongly affect the weathering rate, because the size and placement of continents affects how much of the global precipitation falls on land and sustains continental weathering. We are led to a condition W(P(pCO2), T(pCO2),pCO2) = r, which can be solved for pCO2. Once that is known, everything else is known, and one can then explore the dependence of the resulting climate on slowly varying parameters such as the stellar luminosity, the continental configuration, and the outgassing rate. This is the basic idea behind all CO2 weathering feedback models, and in such models we seek to determine the extent to which the weathering feedback can control temperature and keep it in a habitable range.

Without even writing down a specific form of W, we can obtain a very important general result in a special case. Namely, if the weathering rate is not explicitly dependent on pCO2, and if the precipitation depends only on temperature and not directly on the supply of absorbed stellar energy, then the equilibrium condition is simply W (P (T), T)) _ r. This means that for any given outgassing rate and stellar luminosity, the temperature must adjust to a fixed value. In particular, this temperature doesn't change as the star gets brighter over time. In this case the weathering feedback acts to control climate perfectly, and the planet's temperature changes only as a result of either the outgassing rate or the continental configuration changing. What happens in this regime is that the requirement of weathering balance fixes T, and then pCO2 must take on whatever value is necessary to achieve this T. For example, when the Sun is dimmer, pCO2 must take on a higher value so as to make up for the reduced solar energy. Conversely, when the Sun is brighter, pCO2 must take on a lower value. The thermostat can break down on the cold end if the required amount of CO2 exceeds the supply. The temperature regulation may also break down at the cold end if the planet falls into a Snowball state. Conventional wisdom has it that silicate weathering ceases in this regime, allowing CO2 to build up to where the planet thaws. However, seafloor weathering will continue, and if it is effective enough it could prevent the planet from every warming up sufficiently to escape the Snowball state. On the hot end, the thermostat can break down if the amount of CO2 required to achieve temperature T falls all the way to zero. At this point, further increases in luminosity will cause the temperature to increase. The planet does not immediately go into a runaway greenhouse at this point, but if the planet has an ocean (as it must, if we are to have silicate weathering at all) then the water vapor feedback will ultimately lead to a runaway once the luminosity exceeds the runaway threshold.

Now let's return to the general case, including the direct effect of pCO2 on weathering. Putting all the effects together, the weathering rate can be represented by the empirical expression

Wo Po Po Tu where W is the weathering rate P is the rate at which rain falls over rocks (the runoff), p is the partial pressure of CO2 in the atmosphere and T is the temperature of the surface at which weathering is taking place. Wo is the weathering rate for the reference state with runoff Po, carbon dioxide partial pressure po and temperature To. a, ft and TU are empirically determined constants. The last of these represents the direct temperature sensitivity of the Urey-Ebelman reactions. Based on values that have appeared in the literature, we adopt a _ .65, b _ .5 and TU _ 10K.

To complete the determination of the weathering rate, we need to determine T as a function of the absorbed stellar radiation and pCO2 . In the calculations to follow, we do this using the polynomial OLR fits described in Chapter 4. The OLR curve chosen was based on Earth gravity, with an assumed relative humidity of 50%. In determining the absorbed stellar radiation, we'll assume an albedo of 0.2, which approximates Earth's, adjusted for the greenhouse effect of clouds. We also need to know how P depends on temperature. One reasonable choice would be to make it increase in proportion to Clausius-Clapeyron. However, calculations with comprehensive dynamic climate models tend to indicate that precipitation increases less rapidly than Clausius-Clapeyron, even before the limitation due to surface shortwave absorption is encountered. Thus, we'll take P/P0 _ 1 + aP • (T — To), with aP _ .03. With these specifications we can solve W/Wo _ r/ro and determine how the pCO2 and temperature change as the luminosity is changed. We will see how effectively the weathering thermostat can offset the Faint Young Sun, now that we have included the explicit pCO2 dependence. According to the conventional wisdom, we are now studying the case of a planet for which the continents are abiotic.

The temperature and CO2 as a function of the stellar constant are shown in Fig. 8.2. To is taken to be near the Earth's present-day temperature, and the outgassing rate is held constant at the value that balances weathering at this temperature. These calculations do not include the effects of ice-albedo feedback, which properly should enter in the cold conditions encountered when the star is faint. For comparison, the figure also shows what the equilibrium temperature would be if there were no silicate weathering thermostat and the CO2 remained fixed at its baseline value. The results show that the CO2 rises to very high values at early times when the star is faint - nearly 100mb, or about 10% of an Earthlike atmosphere. However, because the weathering increases so much at high pCO2, the balance can be achieved with quite low temperatures. The temperature falls to 270K, which is only slightly warmer than the 250K value it would have in the absence of a weathering thermostat. It thus appears that, without some modification of the picture by land plants or some other way to get rid of the explicit pCO2 dependence of weathering, the weathering thermostat does not go very far to resolve the Faint Young Sun problem. With the abiotic pCO2 dependence, the silicate weathering thermostat leaves the Early Earth in a very cold state, unless the outgassing rate is considerably higher at that time.

One can also see the moderating effect of the weathering thermostat on the warm side, as the star gets brighter. When the star is 30% brighter than its baseline value, the pCO2 has fallen all the way to .002mb, or 2 ppmv, and the temperature has risen to 311K. This compares to the temperature of 323K that would occur in the absence of the weathering thermostat. At this point, there is hardly any CO2 left in the atmosphere, and there is limited scope for the weathering thermostat to defend the planet against further increases in the luminosity of its star.

If it really is true that land biota affect the explicit pCO2 dependence as much as conventional wisdom suggests, then the implication is that land biota play a crucial role in planetary climate regulation. With land biota suppressing the explicit pCO2 dependence of weathering, the climate regulation is nearly perfect. Without land biota, the silicate weathering thermostat moderates the influence of stellar luminosity on temperature change, but the regulation is not particularly tight, and on Earth one would have to invoke an increase in outgassing or some other effect in order to account for why the planet was not frozen during the Faint Young Sun - though, to be fair, the thermostat does bring the planet much closer to the temperature where a snowball could be avoided. For Earth, the question of when the thermostat became very efficient is tied in with the question of whether the suppression of pCO2 dependence requires land plants (which only entered the picture about 300 million years ago), or whether bacterial colonization of land would be sufficient. The latter would extend the portion of Earth history for which the thermostat is efficient. The overall scenario including the evolution of land biota would go something like this: Early in the planet's history, there are no land biota and the thermostat is only moderately effective. The Faint Sun period would be very cold, though perhaps not completely frozen. As the luminosity increases, the planet would get considerably warmer, perhaps to conditions much warmer than the present. Then land biota evolve, greatly increasing the efficiency of weathering and eliminating the explicity pCO2 dependence. At this point the planetary temperature drops sharply, but the reduction of weathering in cold, dry conditions prevents a Snowball state. Thereafter, the weathering thermostat becomes very efficient, and further changes in temperature are suppressed, until the required pCO2 drops so low that temperature regulation ceases.

In Chapter 4 we discussed the classic dry-runaway greenhouse, in which the entire ocean evaporates into the atmosphere. However, if a planet fails to meet the criterion for a total dry-runaway (perhaps due to cloud or subsaturation effects), it may nevertheless get hot enough that it can lose a great deal of water vapor to space, despite retaining a liquid (but still hot) ocean. This is known as a wet runaway state, and it is the prevailing view of the path taken by Venus.

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