The A Priori Method

A third approach, not dependent directly on either rock abundance or carbon and sulfur isotopic data, has been used for calculating changes in atmospheric O2 over time. Most of the models consider the cycles of the nutrients, P and N, and how they bring about negative feedback stabilization of O2 level. (Such feedbacks, as they affect marine organic matter burial, are illustrated in figure 3.1 of chapter 3.) The model of Hansen and Wallmann (2003) for the past 150 million years uses the a priori approach and formulates the effects of various processes on burial, weathering, and degassing fluxes including the use of modifying nondimensional (f) parameters like those discussed in this book. They calculate not only O2 but CO2 and the composition of seawater over time. In their model the burial of organic carbon is assumed to be proportional to the rate of supply of phosphorus to the oceans, which arises from the weathering of organic matter, silicates, and carbonate and is inversely proportional to atmospheric O2. In terms of the nomenclature of the present book (see table 5.1):

where O2 is the mass of O2 in the atmosphere, m is an arbitrary parameter (0 to 1), and (0) refers to quaternary average values. For pyrite burial Hansen and Wallmann assume

where rmar = fraction of total organic burial occurring in marine sediments ran = fraction of marine organic burial occurring in anoxic sediments S/C = pyrite sulfur/organic carbon burial ratio (assumed constant).

The oxidative weathering of organic matter and pyrite is assumed to follow

Hansen and Wallmann (2003) separate true weathering from oxidation of reduced gases produced by thermal decomposition during volcan-ism, metamorphism, and hydrothermal reactions occuring at mid-ocean ridges. Expressions for the thermal reactions are numerous and are not repeated here.

Hansen and Wallman (2003) use carbon and sulfur isotopic data, but only to guide their modeling. They calculate values of 813C and 834S over time and then adjust parameters (such as m in equation 6.18) to get the best fit with measured values. For both isotopes this results in excellent agreement with measurements, giving strong backing to the model assumptions. One problem with applying their model to longer periods is the assumption of a constant C/S ratio for organic matter burial. During the Paleozoic there were great changes in C/S due to shifting deposition of organic matter between anoxic (euxinic) basins (low C/S), terrestrial coal swamps (very high C/S), and normal (non-euxinic) marine sediments (intermediate C/S) (Berner and Raiswell, 1983; see also figure 3.2).

Another a priori model is that of Lenton (2001). This model is actually only an addition of modifying factors to the Phanerozoic rock abundance model of Berner and Canfield (2001). He ignores pyrite burial and weathering and multiplies the right side of equation (6.14) by a factor representing the effects of plants on the weathering release of phosphate. The idea is that phosphorus is the limiting nutrient for organic carbon production and burial and that more P release by weathering brings about greater organic matter burial (see figure 3.1). Plant abundance, and therefore the rate of P weathering, is constrained by the effect of O2 on plant productivity and fire frequency. This provides negative feedback to constrain excessive O2 variation, an idea also suggested by Kump (1988) for P release by forest fires. Unfortunately, Lenton's model is not physically correct because the original model of Berner and Canfield (equation 6.14) is for actual measured organic C in sediments, and the calculated Fbg value cannot be arbitrarily varied with modifying factors.

Bergman et al. (2003) have presented an a priori comprehensive model for the entire Phanerozoic that tracks both atmospheric O2 and CO2 and the composition of seawater with time. Factors considered by the modeling include the cycles of C, S, P, and N, interactive marine and terrestrial biota, changing solar insolation, metamorphic and volcanic degassing, tectonic uplift, apportioning carbonate burial between shallow and deep marine sediments, land plant evolution, and plant-assisted weathering. In several aspects the model resembles the GEOCARB model, but it is more complex in considering the atmosphere separately from the oceans and tracking seawater composition. A similar GEOCARB-like approach has been presented by Mackenzie et al. (2003) in a model for Phanerozoic O2, CO2, sediment chemistry, and seawater chemistry. Their model is the most complex to date, and they add a host of new processes. They consider the cycles of C, S, Al, Si, Ti, Ca, Mg, Cl, Fe, K, Na, P, and Si and divide their system into five reservoirs: shallow and deep cratonic carbonate and silicate rocks and sediments, seawater, the atmosphere, oceanic sediments and basalts, and the shallow mantle. They also consider the following processes: continental and seafloor weathering of silicates and carbonates, sedimentary dolomite formation, net ecosystem productivity, seawater-basalt exchange, precipitation and diagenesis of chemical sediments (including formation of new silicates by "reverse weathering"), redox reactions involving C, S, and Fe, and subduction-decarbonation reactions.

Organic Gardening

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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