Many field experiments have relied on non-isotopic techniques for creating carbon budgets. In these experiments, carbon inputs are modified and the temporal changes in SOC are measured (Larson et al. 1972). Based on these changes, SOC maintenance rates are calculated. Maintenance calculations are based on the relational diagram shown in Fig. 8.1. In this diagram, non-harvested crop residues (NHC) represent the annual additions of organic carbon added to soil. A portion of NHC is converted into SOC. The rate constants (kNHC and kSOC) represent the rate that carbon is transformed from NHC into SOC or SOC to CO2. The relational diagram is used to define several equations. The first equation is 8SOC/8i = 0 at the equilibrium point. For this equation to be true at equilibrium, the amount of NHC

transformed into SOC is equal to the amount of SOC transformed into CO2. Mathematically this is expressed as, kSOC SOCe = kNHC

where SOC is the amount of SOC at equilibrium, NHC is the non-harvested C

e 1 m maintenance requirement (the amount of crop residues that must be returned to maintain current SOC levels), and kSOC and kNHC are first-order rate constants.

If the temporal change in SOC is small (near equilibrium), then the relationship can be defined as dSOC = kNHC [NHCa - NHCm ], (8.2)

where NHCa is the amount of non-harvested C applied. This equation can be rearranged into the form dO = kNHcNHCa -kNHCNHCm. (8.3)

This equation can be converted to a linear equation, y = mX - b, by defining dSOC/dt as y, NHCa as x, and kNHC as m (Fig. 8.2). This derivation provides the theoretical basis for the maintenance requirements reported by Johnson et al. (2006). An important consideration of this derivation is that the y-intercept is the product of the NHC first-order mineralization rate constant (kNHC) and the NHC maintenance (NHCm) requirement, whereas the slope is the NHC rate constant

Clay et al. (2006) proposed an alternative maintenance calculation approach. This approach was also based on the flow chart shown in Fig. 8.1. The derivation of this approach is as follows. As already defined, the kNHC and kSOC represent the first-order rate constants for the transfer of fresh NHC to SOC and SOC to CO2, respectively. Based on the flow chart (Fig. 8.1), three equations were identified. The first two equations were described above. The third equation, NHCa = NHCm + (NHCa -NHCm), is the equality which is used to create the new SOC maintenance equation. The new equation,

Fig. 8.3 A graphical representation of the maintenance calculations used derived by Clay et al. (2006)

Fig. 8.3 A graphical representation of the maintenance calculations used derived by Clay et al. (2006)

NHCa SOC.

kSOC SOCe kNHC SOCe dSOC dt kNHC SOCe

was developed by replacing (NHC - NHC ) with dSOC 1

and NHC with

SOCe' After dividing both sides by SOC and cancelling units, the equation

ksoc dSOC

e NHC

dt kNHC SOCe

t k was derived. This equation was solved by defining SOCimtial as SOCe,

NHC dSOC

-— as y,and- as x (Fig. 8.3). SOC was replaced with SOC because

SOCmMdy dt ^ ' e P i as time approaches infinity, SOCinitial approaches SOCe. The resulting y-intercept is k 1

and the slope is --——-. Based on these values, maintenance requirement kNHC kNHC SOCinitial and first order rate constants are determined with the equations,

The advantages of the Clay et al. (2006) approach are that site-specific rate constants are calculated which can be used to calculate the impact of management on carbon turnover (Fig. 8.3). For example, based on Eq. 8.1, if kSOC = 0.011, kNHC = 0.13, and NHC = 4,000 kg C (ha year)-1, then SOCe is 47,300 kg C ha-1 [47,300 = (0.13/0.011)(4,000)]. If NHC is reduced to 2,000 kg C (ha year)-1 then SOC will decrease to 23,600 kg ha-1. The disadvantages with the Larson et al. (1972) and Clay et al. (2006) approaches are that they assume that: (1) above- and below-ground biomass make equal contributions to SOC, (2) the amount of below-ground biomass is known; (3) SOC is near the equilibrium point; and (4) the rate constants are constant. Numerous studies have shown that above- and below-ground biomass have different mineralization rate constants (Barber and Martin 1976; Huggins et al. 1998). If below-ground biomass mineralization rate constants are less than above-ground values, then the importance of above-ground values will be overestimated. In addition, accurate measurements of each pool contributing to the total amount of non-harvested biomass are needed. In almost all situations, the amount of below-ground biomass is unknown.

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