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Modelling the dynamic of organic matter

Modelling allows us to predict over the longer term the change in OM levels in soils on which spreading has been carried out. The Hénin-Dupuis model (1945) and the RothC model are used to simulate the change in OM stocks over the long term. Their simulated results match the changes measured in the field during the first 8 years of the experiment.

The Hénin-Dupuis model


The models usually look at sections whose change dynamic follows exponential kinetics. The simplest model is proposed by Hénin-Dupuis (1945), in which a single section of organic matter (OM) is considered in the soil, as well as for each of the flows by which OM enters into the soil. The humic balance calculations shown in the section Humic balance in spreadings are based on this model.
This model was used to simulate the potentials of C storage in the soils according to changes in crop practices. It has the advantage of requiring few parameters.
If crop practices are maintained, the dynamic of C in the soil is expressed based on the following relationship:


: The sum of annual average C inputs (crop residues and OWP, in t C/ha)


: The balanced stock of C in the ploughed layer (in t C/ha)


: The initial stock of C in the ploughed layer (in t C/ha)


Figure 1. Hénin-Dupuis

Application to the QualiAgro test

Changes in the stock of C in the soil are calculated according to this model. Before spreadings, the C content in the soil was 10 g C/kg of soil. Subsequently, as spreadings were carried out this content reaches balances of 14, 17, 19 and 20 g C/kg soil respectively for the MSW, GWS and BIO compost and FYM treatments. Balance is achieved after around 200 spreadings. With no spreading (control plot), C levels in the soils decrease by 5 g C/kg of soil.

RothC model


The Hénin-Dupuis model only considers a single section of OM in the soil. However, due to the diverse nature of this OM, several dynamic sections can justifiably be taken into account.

In the RothC model, three sections are taken into consideration to represent the different types of OM:
- BIO: the microbial biomass
- HUM: active humified OM
- IOM: inert OM

Three different sections are also identified to describe the type of OM entering into the soil (OWP and crop residues combined):
- DPM: decomposable plant material
- RPM: resistant plant material
- HUM: OM directly integrated into the HUM section of the soil.

The average residence times for these sections in the soil are 1.2 months for DPM, 3.3 years for RPM, 1.5 years for BIO, 50 years for HUM and infinite for IOM.


Figure 2. RothC model

Application to the QualiAgro test

The distribution of OM from composts in the RothC sections is calculated based on an optimisation procedure that uses kinetics of change in the surpluses of C stocks in the soils receiving OWP (Table 1). The OM from OWP is solely distributed between the DMP and RPM fractions. The RPM fraction increases in step with the lignin content of the OWP, which is often used in models to characterise the dynamic sections of OM. However, the RPM fraction is three times higher than the lignin fraction. The OMSI is closely correlated with the RPM fraction and is of the same order of magnitude. Meanwhile, the BSI is not so closely correlated.

Based on RothC simulations, the proportion of residual C after 10 years of OWP application at a biannual frequency is calculated (Table 1). Inputs of MSW compost generate the highest incorporation of degradable OM into the soil, while BIO compost generates the lowest. OWP, having highly biodegradable OM like MSW compost, generate a lower increase in the soil OM stock than composts more resistant to mineralisation.

Table 1. Proportions of fractions that are easily decomposable (DMP) and resistant to degradation (RPM) in distributed OWP, optimised using the RothC model; r² coefficient of determination for adjustments using RothC; and calculation of the total proportions and in the OM sections in the soil (HUM + BIO) of C from OWP remaining in the soils after 10 years of inputs every two years


Figure 3 shows the change in C levels in the plots receiving OWP compared with the control, in treatments receiving N input. These values during the first eight years of the experiment match the values predicted by the model. These correspond to between 34% and 58% of the C input by OWP (Table 1).


Figure 3. Modelling of the C stock in the soil with RothC, for the GWS+N and MSW+Ntreatments, comparison with the measured values. The lines represent the levels calculated by the model. The shapes (squares and triangles) correspond to the values measured in the soil