## Mineralization Kinetics

Once the carbon inputs are known or estimated, several different methods can be used to determine carbon turnover. SOC turnover can be described using zero and first-order kinetics (Paul and Clark 1989). For zero-order kinetics, the temporal change in the substrate concentration (8SOC/8t) is defined by the equation dSOC

-= -k dt where k is the rate constant. After integration the equation is written as

SOCt = SOCimtial - kt where SOC, is the amount of SOC at time t and SOC., is the amount of SOC at t initial the beginning of the experiment. For zero-order equations, the mean residence time (MRT) and half-life (T1/2) residence are MRT = SOCmtJk and T1/2 = SOCinitial/(2k).

For systems where the mineralization rate is dependent on the substrate concentration, first-order kinetics can be used to describe carbon turnover (Paul and Clark 1989; Six and Jastrow 2002). The first-order rate equation is

dt which, when integrated, results in the equation

SOC, = SOCimtiale

For first-order rate equations, the MRT (MRT = 1) and half-lives can be calculated

0 696 k (t = —-). However, these relatively simple equations may not explain the k complexity observed in natural systems (Baisden et al. 2002). To solve this problem the CENTURY model (http://www.nrel.colostate.edu/projects/century5/) divides SOC into active, slow, and passive soil carbon pools. The active pool represents microbial biomass with a turnover time of days to years. The slow pool represents more recalcitrant material with turnover times in years to decades. The passive pool is humified carbon stabilized on mineral surfaces with turnover times of hundreds to thousands of years. Each pool has different rate constants and, therefore, different MRT. As rate constants decrease, there is a concomitant increase in MRT. For example, if a pool has an annual rate constant (k) of 0.66 g (g year)-1, the MRT would be 1.5 years, whereas a pool with k of 0.04 g (g year)-1 would have an MRT of

25 years. This CENTURY model has been used to assess carbon turnover in a wide range of environments (Parton et al. 1993; Gilmanov et al. 1997).

The Rothamsted Carbon Model (RothC) uses a five pool structure, decomposable plant material (DPM), resistant plant materials (RPM), microbial biomass, humified organic matter, and inert organic matter to assess carbon turnover (Coleman and Jenkinson 1996; Guo et al. 2007). The first four pools decompose by first-order kinetics. The decay rate constants are modified by temperature, soil moisture, and indirectly by clay content. RothC does not include a plant growth sub-module, and therefore NHC inputs must be known, estimated, or calculated by inverse modeling. Skjemstad et al. (2004) tested an approach for populating the different pools based on measured values.

Many scientists have investigated chemical methods to define these pools (Wolf et al. 1994; Olk 2006; Olk and Gregorich 2006; Zimmermann et al. 2007). Zimmermann et al. (2007) reported that there is a good correspondence between extracted soil fractions and the carbon pools used in the RothC model. Olk and Gregorich (2006) stated that "each procedure has its strengths and weaknesses; each is capable to some degree of distinguishing labile SOM fractions from nonlabile fractions for studying soil processes, such as the cycling of a specific soil nutrient or anthropogenic compound, and each is based on an agent for SOM stabilization. Physical fractionations capture the effects on SOM dynamics of the spatial arrangement of primary and secondary organomineral particles in soil, but they do not consider chemical agents for SOM stabilization. They appear better suited for C cycling than N cycling. Chemical fractionations cannot consider the spatial arrangement, but their purely organic fractions that are suitable for advanced chemical characterization and can be used to elucidate molecular-level interactions between SOM and nutrients or other organic compounds. During all fractionations, the potential exists for sample alteration or mixing of material among fractions." The general conclusion of many studies is that low-density soluble SOC turns over faster (i.e., has a higher k value) than high-density mineral-associated SOC, and hydrolyzable SOC turns over faster than non-hydrolyzable SOC (Martel and Paul 1974; Six and Jastrow 2002).

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