Additional experiments conducted

As the POLOUD model is based on statistical regressions, it was crucial to gather enough data, covering a wide diversity of EOM biochemical characteristics to achieve a robust calibration and increase the model universality. We thus conducted additional experiments.

3.3.2.2.1.Soil

The soil used for the EOM incubation study was sampled from the surface layer of an experimental field of INRA (Institut National de Recherche Agronomique) cropped farm, at Le Rheu, near Rennes (France). It was classified as a Luvisol-Redoxisol (Baize & Girard, 2008) with 146 g.kg^-1 clay, 693 g.kg^-1 silt and 161 g.kg^-1 sand. Organic carbon content was of 11.9 g.kg^-1 and pH in water of 6.1 (Tableau 29).

3.3.2.2.2.Exogenous organic matter (EOM)

Twelve organic amendments (Tableau 28) were incubated in the soil, in two series. The first one concerned fresh solid manure from a finishing steer feedlot (MAN), the solid phase of the digestate obtained from the anaerobic digestion of this manure (ADMAN), the compost obtained from this manure treated in continuously aerated 300L pilots (CMAN), the solid phase of a digestate obtained from the anaerobic digestion of a biowaste (organic fraction of household waste mixed with green waste) (ADBIO) and the compost obtained from composting of the same biowaste in continuously aerated 300 L pilots (CBIO), a poultry manure (PM), a pig slurry (PS1), a composted pig manure (CP) and a second cattle manure (CM2). The second series concerned the compost of ADMAN (CADMAN), the compost of ADBIO (CADBIO) and an anaerobic digestate of pig slurry (ADPS).

Dose Temperature Water potential Soil OC Clay Silt Sand pH in water Source (g C.kg^-1 dry soil) (°C) (kPa) (g.kg^-1) (g.kg^-1) (g.kg^-1) (g.kg^-1) (dimensionless)

Abiven et al. (2007) 4 25 -60 10.9 95 518 387 7.5

Annabi et al. (2007) 5.12 28 -60 10 170 760 70 6.9

Cosentino et al. (2006) 4 20 -10 9.2 167 562 271 7.0

Le Guillou (not published) 4 25 -30 23.9 160 420 410 6.0

Present study 4 25 -50 11.9 146 693 161 6.1

Soil characteristics Incubation characteristics

193 Analysis of the global EOM was performed on samples ground to 2mm after being solidified by immersion in liquid nitrogen (-196°C) The dry matter was determined by drying at 80°C to constant weight. The TC content was determined by oxidizing C to CO₂ at 1 800 °C and CO₂ was detected by a thermal detector (FLASH 2000 Organic Elemental Analyzer, THERMO SCIENTIFIC).

Biochemical characteristics were analyzed by a method derived from Van Soest (AFNOR, 2009). The first extraction step was achieved by boiling water during 1 hour at a residue/water ratio of 2/17 (w/w) followed by centrifugation (20 min, 17700 rpm). Samples were then passed in neutral detergent to allow the calculation of the SOL fraction. Hemicellulose-like (HEM), cellulose-like (CEL) and lignin and cutin-like (LIC) fractions was automatically analyzed as described by AFNOR (AFNOR, 2009). The OM contents of the residues obtained after each extraction step was analyzed by calcination at 550°C to allow the calculation of the distribution of OM of the global EOM into the biochemical fractions.

3.3.2.2.3.Incubations

The soil was air dried, gently sieved (3 to 5 mm) and its water content was adjusted with ultra-filtered water to reach 80% of the field capacity, namely a water potential of -50kPa.

The EOM were air dried at ambient temperature and ground to 2 mm. Before adding EOM, 180 g of soil was placed in 2L, hermetically closed jars, stored in a dark room at 25°C for one week. Each EOM was then added to the soil at the rate of 4 gC.kg^-1 dry soil. For each treatment (soil without EOM (control) and five soil + amendment mixtures), three replicates and eight destructive samples for analysis were prepared. A beaker with 20 mL of deionized water was placed in each jar to prevent soil drying. Each week during the incubations, the jars were opened for aeration to avoid anoxic conditions. Sample for aggregates stability measurements were collected after 0, 3, 7, 14, 21, 30 and 56 days.

3.3.2.2.4.Aggregate stability

Aggregate stability was measured using the slow wetting test proposed by Le Bissonnais (1996). This method permit to investigate the resistance of soil aggregate to partial slaking process induced by the slow wetting of the air dried aggregates. The AS was expressed as the mean weight diameter (MWD) (mm) of aggregates calculated after the test.

194 3.3.2.2.5.Modelling

The model used in this study is the POULOUD model described in Abiven et al. (2008). It consists in two steps. The first step aims to adjust a lognormal function to soil aggregate stability dynamic for each EOM by fitting three shape parameters, as described in Equation 1.

In order to reduce the effect of the heterogeneity concerning the incubation conditions, the aggregate stability modelled was the difference between the aggregate stability of each treatment (soil + EOM) and the aggregate stability of the control. The fitting was performed by minimizing the root mean square error (RMSE) (Equation 2) of the MWD with the Nelder-Mead algorithm (Nelder & Nelder-Mead, 1965). To avoid aberrant values of the optimized parameters, constraints were included in the minimization function: A was coerced between -2 and 1.5 mm, B between 0 and 1.5 and C between 0 and -20 days.

Equation 1

wN ] = w exp Ù−0.5 × •^-Úi_¨^ÊÌmž Û (1) (From Abiven et al. (2008))

Where : AS(t) is the aggregate stability as a function of time (expressed in mm as MWD), t is the time since the EOM incorporation, (in days) and A, B and C are three shape parameters representing respectively the magnitude (mm MWD), the scale and the duration (days) of the aggregate stability curve.

The second step consists in linking the three shape parameters A, B and C to the biochemical characteristics. In the original model of Abiven et al. (2008), simple regressions were established between each parameter and organic fractions of EOM. Parameter A was found a linear decreasing function of LIC, B was a linear increasing function of HEM+CEL and C of the polysaccharides content. In the present study, we used the partial least squares regression (PLSR) method (Wold et al., 2001) instead of the classical regression by least squares, because PLSR is a recent particularly adapted technique for analyzing collinear variables.

Indeed, in our case both the response variables and predictors were supposed to be potentially correlated. The response variables were the optimal fitted A, B and C shape parameters, as determined for each EOM incubation in the first step of the modelling procedure, and the predictor variables were the biochemical characteristics of the EOM, i.e. the SOL, HEM, CEL, LIC fractions of the EOM plus the total C and N contents of the EOM (Tableau 28).

Unlike in Abiven et al. (2008) we did not included the polysaccharides contents in the regression model, as this information was not implemented in all the considered studies and thus it would have drastically reduced the dataset.

195 Before computing the PLSR, the predictor variables were scaled as they were expressed in different units. The coefficients of the PLSR were then back-transformed to allow the calculation of the shape parameters directly from the EOM characteristic for new observations.

3.3.2.2.6.Evaluation of the model performances

The POULOUD model performance was evaluated by computing the root mean square error (RMSE) between measured and predicted values of mean weight diameters (Equation 2).

Equation 2

NU = ^^∑u$f.F_v^{$JFt ²a}

With: Xi: Measured values of CO₂, mineral nitrogen or microbial biomass; :y_p : Simulated values of CO₂, mineral nitrogen or microbial biomass ; N: Number of measurements.

The PLSR model performance was evaluated by computing the RMSE and the determination coefficient (R²) on each shape parameter.

3.3.3. Results