Atmospheric Greenhouse Effect and Weathering
Changes in the concentration of greenhouse gases affect both the temperature and the hydrology of the continents, which in turn affect the rate of uptake of CO2 via silicate mineral weathering. The principal greenhouse gases of interest are CO2 and CH4. (Although H2O is the strongest greenhouse gas, it is buffered by evaporation and condensation that is driven by external factors such as solar radiation and the CO2 greenhouse effect.) The buildup of CO2 in the atmosphere can lead to higher temperatures, more rain on the continents, more runoff, and thus faster weathering. It is well established that minerals dissolve faster at higher temperatures and with greater rainfall (e.g., Jenny, 1941). Thus, changes in weathering rate induced by variations in CO2 can serve as a negative feedback for stabilizing global temperature (Walker et al., 1981; Berner et al., 1983). This is illustrated in figure 2.4 in terms of a simple systems analysis feedback diagram.
The effect of changes in concentrations of methane can be important to weathering only when it becomes the dominant greenhouse gas. This was probably the case for the Archean (Pavlov et al., 2000) and possibly much of the Proterozoic (Schrag et al., 2002; Pavlov et al., 2003). However, for the Phanerozoic this was unlikely because of the presence of relatively high levels of O2 (compared to the Precambrian). Because CH4 is rapidly oxidized to CO2 in the atmosphere (residence time of atmospheric CH4 is only about 10 years), Phanerozoic levels of CH4 probably never were high enough over sufficiently long periods to act as the dominant greenhouse gas.
Results of general circulation models (GCMs) for global mean surface temperature versus CO2 concentration can be represented rather well by the simple expression (Berner, 1991):
Figure 2.4. Systems analysis diagram for the greenhousesilicate weathering feedback. In such diagrams arrows with bullseyes represent negative response; without arrows positive response. A complete cycle with an odd numbers of bullseyes means negative feedback and stabilization; a complete cycle with an even number of bullseyes, or no bullseyes, means positive feedback and (normally) destabilization.
Figure 2.4. Systems analysis diagram for the greenhousesilicate weathering feedback. In such diagrams arrows with bullseyes represent negative response; without arrows positive response. A complete cycle with an odd numbers of bullseyes means negative feedback and stabilization; a complete cycle with an even number of bullseyes, or no bullseyes, means positive feedback and (normally) destabilization.
Chemical Weathering of Silicates 27 T(t)  T(0) = r ln RCO2 (2.8)
where
T (t) = global mean surface temperature at some past time T(0) = global mean surface temperature for the present RCO 2 = ratio of mass of CO2 in the atmosphere at time t to that at present r = coefficient derived from GCM modeling.
For the purpose of studying the carbon cycle on a Phanerozoic time scale, the "present" can be assumed to be preindustrial with a CO2 concentration of 280 ppm and a global mean temperature of 15°C.
The effect of temperature on the rate of primary mineral dissolution during weathering can be deduced both from laboratory and field studies. To represent the temperature effect, it is common to employ the "activation energy," which practically is a measured temperature coefficient. The socalled Arrhenius expression used for this purpose is:
where
T = absolute temperature in degrees K
To = absolute temperature for some standard state (here assumed to be 288°C the present global mean surface temperature AE = activation energy R = gas constant
J = dissolution rate in terms of an equivalent weathering uptake of CO2 to form dissolved HCO3. Units are mass per unit volume of soil (regolith) water per unit time Jo = dissolution rate for the standard state.
The results of laboratory studies on silicate dissolution (Brady, 1991; Blum and Stillings, 1995; White et al., 1999), in terms of activation energy, are shown in table 2.2. For mathematical convenience equation (2.9) can be rewritten as:
Because T and To are large numbers that are rather close to one another at earth surface temperatures, their product can be considered as essentially constant, so that, solving for J,
Rock or mineral 
AE (kJ/mol) 
Reference  
Laboratory experiments  
Olivine 
38 
86 
Brady, 1991 (compilation) 
Enstatite 
41 
80 
Brantley and Chen, 1995 
Diopside 
50 
150 
Brady, 1991 (compilation) 
Wollastonite 
72 
Brady, 1991 (compilation)  
Naplagioclase 
60 
Blum and Stillings, 1995  
Kfeldspar 
52 
Blum and Stillings, 1995  
Granite/granodiorite 
47 
60a 
White et al., 1999 
Granite/granodiorite 
53 
71b 
White et al., 1999 
Field studies  
Plagioclase 
77 
Velbel, 1993  
Plagioclase 
97 
Brady et al., 1999  
Plagioclase 
55c 
Brady et al., 1999  
Olivine 
89 
Brady et al., 1999  
Olivine 
48 
Brady et al., 1999  
Granite/granodiorite 
51a 
White et al., 1999  
Basalt 
42 
Dessert et al., 2001 
aBased on silica dissolution. bBased on Na dissolution. cMediated by lichens.
aBased on silica dissolution. bBased on Na dissolution. cMediated by lichens.
where Z is equal to AE/RTTo (symbolized as ACT in Berner and Kothavala, 2001). Equation (2.11) is a form that is especially useful in carbon cycle modeling.
Field studies (Velbel, 1993; Brady et al., 1999; White et al., 1999; Dessert et al., 2001) have shown that for a given rock type one can discern a temperature effect on weathering rate providing that variations in relief and other factors are limited. Results of these studies have been summarized in terms of activation energies and are also shown in table 2.2. In general there is agreement between field studies and experimental studies indicating that the ratelimiting step in the dissolution of the primary minerals is the same in the field as in the lab. Judging by the rather high values for AE, this must involve reactions at the mineral surface and not diffusion of dissolved species to and from the surfaces. (For a detailed discussion of mineral dissolution mechanisms, see Lasaga, 1998.)
To convert weathering fluxes J to riverine fluxes of HCO3 to the oceans, some additional calculations are necessary. First, we need to know the global mean concentration of dissolved HCO3 in river water derived from Ca and Mg silicate weathering. Following Berner (1994), we assume, as a first approximation, that for a "global regolith" at steady state,
where
C = global average concentration of dissolved HCO3 from silicate weathering, in mass per unit volume, in the regolith pore solution and eventually in river water r = global mean runoff (volume per unit time per unit area) A = surface area of that portion of the continents undergoing silicate weathering V = volume of water contained in the global regolith.
where h is the mean thickness of the global regolith, and O is its mean porosity. Combining (2.12) and (2.13) and solving for C,
Now, it has been shown (Berner, 1994) from a variety of field studies of rivers that
This demonstrates the effect of dilution as a result of increasing runoff. The same form of this expression can be independently derived from equation (2.14) (Berner, 1994), resulting in
where k' is a parameter expressing the relation between the mean thickness of the global regolith and runoff. Equation (2.16) is used to convert J to C to determine the global flux of HCO3 from silicate weathering.
In doing carbon cycle modeling, it is important to remember that it is the temperature of the land actually undergoing weathering that is relevant. Thus, the use of global mean temperature (which includes the oceans) as it relates to CO2 level (equation 2.8) is an oversimplification. However, in the absence of available paleoland temperature versus CO2 data, modeling to date has been forced to use this simplification (e.g., Walker et al., 1981; Berner, 1994; Wallmann, 2001). Furthermore, the mean temperature of the land is inappropriate because it includes areas of glaciers or deserts where there is virtually no chemical weathering. An attempt to apply a more rigorous approach, by looking at the relation between CO2 and the temperature of land with precipitation >25 cm/year (no deserts) and a mean yearly temperature >5°C (no glaciers), has been applied to a GCM study of weathering during the Cretaceous (80 Ma) by Kothavala, Grocke, and Berner (unpublished ms).
Besides temperature, rainfall and the flushing of the regolith is also important in weathering. With all other factors held constant, flushing can be represented by runoff from the land. Runoff is affected by changes in both local and global climate. Local climate is a function, on a geological time scale, of continental drift as land areas pass from dry to wet climatic zones. This effect of paleogeography on runoff will be discussed in the next section. Concern here is with the effect of changes in global mean temperatute, due to the greenhouse effect, on runoff. The relation between global mean temperature and runoff can be deduced from GCM models, but to my knowledge this relation has not been calculated for the distant past with paleogeographies different from that at present. Using present geography, Berner and Kothavala (2001) deduced, on the basis of GCM modeling, the expression:
where r represents runoff, T is global mean temperature at some past time, and To is that for the preindustrial present. Y is an empirical parameter fit to the GCM results (symbolized as RUN in Berner and Kothavala, 2001).
Calculation of the global weathering uptake of atmospheric CO2 and riverine flux of HCO3 to the oceans is done according to
where flux is in mass per unit of land area. To normalize weathering to that at present, we have fB(T) = [C(T)/C(To)] [r(T)/r(To)] (2.19)
where fB(T) equals flux (T)/flux (To), the dimensionless parameter expressing the effect of global mean temperature on the uptake of CO2 to form dissolved HCO3 via the weathering of silicates. Assuming that the parameters O and k' do not change with temperature, we obtain from equations (2.16) and (2.19):
To combine the effects of temperature on runoff with that on dissolution rate, we obtain from equations (2.17) and (2.20):
which on substituting equation (2.11) yields fe(T) = exp[Z(T  To)] [1 + Y(T  To)]°.05 (2.22)
Finally, to obtain the greenhouse effect of CO2 on the rate of silicate weathering uptake of CO2 to form HCO3, we combine equation (2.22) with the GCM greenhouse equation (2.8) to obtain the nondimensional greenhouse parameter fBg(CO2) (subscript g stands for greenhouse):
A plot of equation (2.23), which represents the greenhousecaused negative feedback response to changes in atmospheric CO2, is shown in figure 2.5.
Organic Gardening
Gardening is also a great way to provide healthy food for you and your loved ones. When you buy produce from the store, it just isnt the same as presenting a salad to your family that came exclusively from your garden worked by your own two hands.
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