CHAPTER 4: A MATHEMATICAL MODEL
4.2.8. Scenario simulations
The sensitivity of simulations to substrate input and assigned parameter values was established by comparing the outcome of four scenarios representing the addition of two
Parameter Description Model components directly influenced
Flow partitioners
α Respration coefficient Primary flows to GasC 0.55
η Microbial incorporation coefficient Primary flows to BugC 0.30
βLF1 FREE microbial fraction Bug and LF1 0.10
βLF2 INTRA-AGGREGATE microbieal fraction Bug and LF2 0.10
φLF2 Universal flow partitioner Relocation flows to LF2 0.20
φiHF Universal flow partitioner Relocation flows to HF 0.50
ρbug Microbial C-to-N ratio BugN 6.00
θ Assimilable fraction SolNand N limitation 0.30
Reactivity constants
kLF1 Reactivity constant LF1
kLF2 Reactivity constant LF2
kHF Reactivity constant HF
ksol Reactivity constant Sol
kmort Mortality constant Bug
kfix Chemical fixation rate constant SolN
kvol Gaseous N loss rate constant SolN
0.00005 0.0300 0.0150 0.001 0.0005 Assigned value
Table 4.1. List of optimisable parameters invoked in the model and the values assigned to them
in the decomposition scenarios
0.0100 0.0020
Model Parameter
C light1C0 light2C0 heavyC0 solC0 + gasC0 (+) bugC0 +
N light1N0 light2N0 heavyN0 solN0 + gasN0 (+) 13
C light113C0 light213C0 heavy13C0 γgas0 (+) γbug0 + γsol0 +
15
N light115N0 light215N0 heavy15N0 αgas0 (+) αbug0 + αsol0 +
+ independent measurement required
(+) nominal values or background estimates may be used
light1* relate to FREE organic matter
light2* relate to INTRA-AGGREGATE organic matter
heavy* relate to ORGANOMINERAL fraction
sol* strictly relate to NaI soluble organic matter
bug* relate to microbial biomass
Table 4.2. List of variables representing initial values for which numeric values are required
contrasting straw residuesl (bothl C4 landl bothl enrichedl in 15N), l atl twol rates (Table 4.3.). Constant environmental conditions were assumed (temp = 1; moist = 1) and simulations run from 10 days before to 365 days after incorporation of straw. A control scenario (i.e. with no straw addition) was also run.
Initial values
Initial values defined the status of relevant variables and compartments at the beginning of the simulation i.e. 10 days prior to straw incorporation (Day –10). In the scenarios a total soil C content of 20 mg C g-1 was assumed, with its distribution between FREE, INTRA-AGGREGATE and ORGANOMINERAL fractions (represented by
light1C, light2C and heavyC) based on that in the silty clay loam soil fractionated in
Chapter 2 (Table 4.4.). The proportion allocated to SolC was based on the typical proportion measured as dissolved organic carbon (DOC) in arable soils (Gregorich et al.
2000). The equivalent δ13C values (δ*0) reflected the differences in chemical composition of the measured fractions established in Chapter 2, the δ13C of SOM increasing with repeated transformation (Boutton 1996). A value typical for C3 plant material was specified for δlight10 (–28 ‰) and a higher value (close to that of whole soil) for δheavy0 (Table 4.4.). The value used for δSol0 was closer to that of δlight20, DOC being composed of predominantly active, less transformed SOM (Gregorich et al.
2000). Calculated from the sum of the fractions, the initial δ13C of the whole soil was – 26.61 ‰ (Table 4.4.). Values for *13C0were calculated from δ*0 and *C0 according to the equation in Section 5.2.2.2.
Fraction ratio Light1* 5.0 1.0 -27.00 22.0 2.17 0.045 0.3663 Light2* 5.0 1.0 -28.00 20.0 2.39 0.050 0.3664 Heavy* 89.5 17.9 -26.50 9.0 94.96 1.989 0.3670 Sol* 0.5 0.1 -28.00 10.0 0.48 0.010 0.3663 Total 100 20.00 -26.61 9.55 100 2.09 0.3670 Compartment ratio LF1* 4.80 0.96 -26.96 24.8 1.85 0.039 0.3663 LF2* 4.80 0.96 -28.00 22.2 2.07 0.043 0.3664 HF* 87.90 17.58 -26.47 9.1 92.42 1.936 0.3670 Bug* 2.00 0.40 -28.00 6.0 3.18 0.067 0.3664 Sol* 0.50 0.10 -28.00 10.0 0.48 0.010 0.3663 Total 100 20.00 -26.61 9.55 100 2.09 0.3670
Table 4.4. The distribution and isotopic composition of C and N between and within measured SOM fractions assumed for the scenarios (before the straw addition)
% total mg g-1 15N atom% % total mg g-1
% total C-to-N
C-to-N N
Table 4.5. The calculated distribution and isotopic composition of C and N between and within the modelled SOM compartments in the scenarios (before the straw addition)
δ13 C (‰) C mg g-1 15N atom% C mg g-1 δ13C (‰) N % total Scenario HQ/H HQ/XH LQ/H LQ/XH Addition rate (g g-1) 2.0 6.0 2.0 6.0 800 2400 800 2400 15 15 60 60 -12.00 -12.00 -12.00 -12.00 10.00 10.00 10.00 10.00 15 N (atom%)
Table 4.3. The nature of the four straw additions used in the scenarios, encompassing high (H) and
atypically high addition rates (XH) and residues of high (HQ) and low (LQ) quality
C (mg g-1) C:N ratio δ13
The initial distribution of N between the standard fractions (*N0) was calculated from the distribution of C and their designated C-to-N ratios (Table 4.4.). The latter were chosen (as for δ*0) to reflect the contrasting levels of microbial transformation amongst the fractions, lower ratios assigned to the more transformed fractions. Due to the transient nature of mineral N, an arbitrary C-to-N ratio of 10 was used to determine
SolN0. On account of the higher C-to-N ratios expected in FREE and INTRA-AGGREGATE organic matter, the light fractions accounted for a smaller proportion of total soil N than total soil C (Table 4.4.). Although rather insignificant where enriched substrates are simulated, the small general increase in 15N natural abundance with decomposition (Hopkins et al. 1998) was accounted for in calculation of *15N0 from *N0 (Table 4.4).
To calculate the initial magnitude of model compartments from those assumed for the measured fractions, BugC0 was taken as 2 % of total soil C, within the typical range of 1 to 3 % (Theng et al. 1989). The value for BugN0 was determined from BugC0 using ρBug. The isotopic composition of the microbial biomass was assumed equivalent to that of INTRA-AGGREGATE organic matter. Using the numeric values specified for β* (see below), values for LF1*0, LF2*0 and HF*0 were calculated from their measurable equivalents light1*0, light2*0 and heavy*0 (Table 4.5.). Nominal values were used for
GasC0 and GasN0,.
Optimisable parameters
Circumstantial evidence suggests that microbial biomass is a significant and possibly substantial component of light fraction (Gregorich and Janzen 1996). In the scenarios FREE and INTRA-AGGREGATE fractions were assumed to each contain 10 % of
the total soil microbial biomass (i.e. βLF1 = 0·1; βLF2 = 0·1). A value of 6·0 was used for ρBug, typical of a predominantly bacterial community (Theng et al. 1989).
A typical value of 0·45 was assumed for microbial efficiency, with the corresponding value for η (incorporation) set arbitrarily at 0·30; the balance between incorporation and relocation flows have not been explored experimentally. The values assigned to φLF2 and φHF (governing the sub-division of relocation flows) were intended to reflect the greater magnitude of heavyC, offset against the higher likely reactivity of light fractions (φHF = 0·5; φLF2 = 0·2). The utilisation of the C and N substrate compartments is broken down in Figure 4.6., using the example of LF1.
The values assigned to kLF1, kLF2 and kHF (Table 4.2.) were intended to reflect the contrasting reactivity expected of fractions differing in their physical association and chemical composition. The assigned values gave mean residence times of 100, 500 and 20 000 days for LF1, LF2 and HF respectively, compatible with the concept that FREE organic matter is dynamic on a seasonal timescale, INTRA-AGGREGATE over years, and ORGANOMINERAL over decades. The value assigned to kmort reflects the high rate of microbial turnover established experimentally and through parameterisation of existing models (50 % greater than that of LF1 in this scenario). The mobile Sol compartment was assumed to be twice as active as the microbial biomass (giving a mean residence time of 33 days).
The value assigned to θ suggests one-third of soluble N is available for direct assimilation by microbial cells as NH4+ or low molecular weight compounds to balance their demand for N. This is based on the typical difference between mineral N and total
[Figure 4.6 – C flows from LF1]
Figure 4.6. The general relationship between C and N flows from substrate
compartments using the example of the LF1 and parameter values used in the scenarios.
Equivalent flows from Bug represent physical relocation with microbial mortality and
occur at the C-to-N ratio of Bug (ρbug) with no Gas component
Organic
inputs
N
C
LF1C
GasC
BugC
η (30 %)
φ(15 %)HF(50 %)(1 - η= - 7.5 %α) xBugN
(C flow) / (ρbug), or else
(C flow) / (ρLF1)
α
(55 %)
SolN
SolC
LF2C
Supplementary (balancing) N flow for LF1
0 or: (LF1C flow) / (ρbug)
- (LF1C flow) / (ρLF1)]
LF2N
φiLF2 x excess LF1N flow:
0 or: N flow - ( LF1Cflow) / (ρLF1)
(1-φLF2-φHF) x excess LF1N flow:
0 or: (LF1C flow) / (ρLF1)
- (LF1C flow) / (ρbug)
HFC
φHF x excess LF1N flow:
0 or: N flow - ( LF1C flow) / (ρLF1)
(15 %) (1-η-α) x (1-φLF2-φHF) (40 %) =6 %
HFN
LF1N
(15 %)(1 - η-α) x φLF2(10 %)= 1.5 %soluble N (TSN) measured in the field. In the scenarios, nominal values were assigned to kvol (governing gaseous N loss) purely to provide a sink for SolN. Since there is little existing data to qualify or quantify chemical fixation flows (from SolN to substrate compartments), kfix was assigned a value of 0.
Substrates
The C-to-N ratio of active substrate compartments strongly influences immobilisation activity, and largely determines the demand for supplementary N. The scenarios encompass two types of straw of contrasting C-to-N ratio. The low quality (LQ) straw had a higher C-to-N than wheat straw (close to that of maize), that of the high quality (HQ) straw a C-to-N similar to that of rye grass (Table 4.3). A δ13C value characteristic of C4 plants (Smith and Epstein 1971) was used for both straw types to simulate the tracing of C using the natural abundance method (Section 1.5.2.). The lower incorporation rate (H) equated to a high field-rate of approx. 6 t dry matter ha-1 (assuming a soil bulk density of 1.30 kg L-1 and a topsoil depth of 23 cm). The alternate rate (XH) was more extreme, corresponding to a field rate of approx. 18 t dry matter ha-1. The additions were made to LF1* rather than light1*, since the latter has a microbial component (Section 4.2.2.).