## Simple Models

The kinetics of plant nutrient transformations has been of interest for a long time, particularly the kinetics of N mineralization. Stanford and Smith (1972) began by describing net N mineralization using a simple first-order model, N = N0(1 _ e_kt), where N is the amount of nitrogen mineralized at time t and N0 is the amount of potentially mineralizable nitrogen. Several modifications to first-order models, as well as other kinetic models, have been proposed to account for experimental observations of large initial flushes of mineralization or for lags before the initiation of mineralization (Ellert and Bettany, 1988). In selecting a model for N and S net mineralization, one should generally increase model complexity incrementally to obtain a suitable fit, keep the number of parameters to a minimum, and know that no single model will fit data for all soils under all conditions, while some conditions will be adequately described by several models.

Because they play different roles in plants and the environment that lead to differing dynamics, there are few short-term or single-season models for C like there are for N and other plant nutrients. Soil organic matter models generally project the long-term sustainability of changes in soil C, but there are a number of ways to describe the short-term decomposition of organic residues during the first few months after introduction to the soil. Field and laboratory experiments have shown that initial decomposition rates of litter are generally independent of the amount of biomass added unless it exceeds 1.5% of the dry soil weight. Decomposition of plant residues has been experimentally found to be reasonably well described by first-order rate kinetics. The use of first-order kinetics to describe the decomposition of SOM implies that the microbial inoculum potential of soil is not limiting the decomposition rate (e.g., X0 >> S0, from the previous section). This is true, in large part, because soil microbial biomass often has a fast growth rate relative to the length of most decomposition studies.

Jenny (1941) published a simple model that used a combination of zero-order and first-order components to describe changes in soil organic matter,

dt where X is the organic C or N content of the soil and A is the addition rate (mass t_1) used to describe accumulations or losses not associated with decomposition. However, this model does not account for the heterogeneous nature of SOM, i.e., k is constant. Several approaches have been used to accommodate for the changing nature of organic matter during decomposition, such as making k a function of time or including additional compartments.

Experimental data for the decomposition of added plant residues or manures can be closely fit using the summation of two first-order equations in the general form

-k.t i D 0_k„t where C is the soil C content at any given time, A and B are the proportions of the two pools, and kA and kB are the first-order constants for each of the pools. In the case

Time (days)

FIGURE 16.3 The fit of the sum of two first-order curves describing C mineralization in soil from a manured and fertilized long-term plot during a 220-day incubation.

Time (days)

FIGURE 16.3 The fit of the sum of two first-order curves describing C mineralization in soil from a manured and fertilized long-term plot during a 220-day incubation.

illustrated in Fig. 16.3, the first pool of the manured treatment represented 5% of the soil C and had a turnover time of 40 days in the laboratory. The second pool represented 45% of the C with a laboratory turnover time of 3 years. The curve representing the fertilized plots showed that the first pool represented 2% of the C with a turnover time similar to that of the manured (40 days). The second pool representing 48% of the C had a turnover time of 5 years. The remainder of the C was known from 14C dating to have a turnover time of 500 to 1000 years and therefore did not contribute CO2 to the decomposition of the inputs. The example demonstrates how the partitioning of organic matter between labile and more resistant fractions alters the decomposition dynamics. Lack of participation of a significant proportion of the soil C in respiration suggests the need for an additional pool or compartment, and this knowledge led to the development of the multicompartmental models.

Differences in the ability of simple models to model short-term versus long-term decomposition dynamics were highlighted by Sleutel et al. (2005), who compared the performance of first-order, sum of first-order, combination of zero-order and first-order, second-order, and Monod kinetic models for extrapolation from short-term data. They concluded that the sum of first-order and Monod models performed best in estimating stable organic C, but did not fit short-term mineralization well, while the first-order and combination of zero-order and first-order models should not be used for extrapolating from short-term data.

Only a portion of the actual decomposition is accounted for when determining the decomposition rate (k) by measuring CO2 output or the amount of C left in the soil.

TABLE 16.2 First-Order Decay Constants with and without Correction for Microbial Biosynthesis during the Decomposition of Organic Compounds Added to Soil under Laboratory Conditions k (day"1)

TABLE 16.2 First-Order Decay Constants with and without Correction for Microbial Biosynthesis during the Decomposition of Organic Compounds Added to Soil under Laboratory Conditions k (day"1)

(days) |
Uncorrected |
Corrected for CUE = 20% |
Corrected for CUE = 60% |

Straw-rye |

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