2.1. Site of the Experiment
[5] The experiment was conducted at the paramo site of Gavidia (8°35′N–8°45′N, 70°52′W–70°57′W) in the Andes of Mérida (Mérida State, Venezuela) at an altitude of 3400 m. The mean annual precipitation is 1329 mm, with a dry season between November and March and a rainy season between April and October. The mean annual temperature is 8.5°C differing only by 1.5°C between the coldest and the warmest months but with a mean daily thermal amplitude of 10.5°C. The experiment was set up in (1) a 2yearold fallow plot (F2y data series) with an estimated soil cover = 0.85 of mainly perennial herbs and (2) in a 7yearold fallow plot (F7y data series) covered by the characteristic paramo giant rosettes and by shrubs (height = 1 to 1.5 m, estimated soil cover = 0.9, differing markedly from grassland). The soil (humitropepts, USA Soil Taxonomy) is loamy and well drained. In the 0 to 10cm layer, sand = 54%, silt = 31%, clay = 15%, pH(H_{2}O) = 4.5, waterholding capacity (v/v) = 0.52 (mean values of the two experimental plots), C = 9.4% (plot F2y) and 8.8% (plot F7y), and N = 0.55% (F2y) and 0.56% (F7y). The high organic matter content explains the high waterholding capacity. The cultivation system is based on a long fallow period used for extensive grazing (generally lasting from 5 to 10 years) alternating with a short (1 to 3 years) potato and cereal cropping period.
2.2. ^{14}C and ^{15}N Labeled Plant Material
[6] A low Nrequiring old cultivar of spring wheat (Florence Aurore) was grown from seed to maturity in a labeling chamber with controlled ^{14}CO_{2} atmosphere (0.03% v/v, 0.86 kBq mg^{−1} C), temperature, radiation, and alternate lighting conditions. The plants, which were cultivated in pure sand, were periodically flooded with a complete nutrient solution containing Ca(^{15}NO_{3})_{2} (10% atomic ratio) as the sole N source. At ear emergence the wheat was dried at 40°C. Only the stems and leaves were used in the experiment. They were ground into particles between 2 and 7 mm long and mixed to obtain a homogeneous material. The C content of the material was 43.0 ± 0.39% (0.821 ± 0.022 kBq mg^{−1} C), the N content was 1.60 ± 0.05% (^{15}N isotopic ratio = 9.250 ± 0.451%), and the C/N ratio was 26.9 ± 0.9. The biochemical fractions of the straw [van Soest et al., 1991] were as follows: neutral detergent soluble = 0.36, hemicelluloses = 0.25, cellulose = 0.26, lignin = 0.03, and ashes = 0.10. The N content of the straw used in the present part of the experiment was relatively high, but the behavior of the model from a litter with low N content will be discussed elsewhere (work in preparation).
2.4. Data Acquisition
[8] At sampling, the wet sample was homogenized and 3 × 5 g wet soil was dried at 105°C for the measurement of the moisture content. The remaining wet soil was subsampled for analyses of (1) microbial biomass^{14}C and ^{15}N (four field replicates × two analysis replicates for MB^{14}C, four field replicates for MB^{15}N), and (2) total^{14}C, (four × eight replicates) and ^{15}N (four × two replicates). Microbial biomass was measured according to the fumigationextraction method of Brookes et al. [1985]: 20 g soil, 150 mL 1 mol(K_{2}SO_{4})L^{−1} extractant, ^{14}C measurement on the extracts by liquid scintillation counting (Tricarb 1500, Packard), measurement of N and ^{15}N by Kjeldahl procedure and isotope mass spectrometry (Finnigan delta S), k_{eC} (the microbial biomassC correcting factor) = 0.45 [Joergensen, 1996], and k_{EN} (N correcting factor) = 0.54 [Joergensen and Mueller, 1996]. Total C and ^{14}C were measured simultaneously using Carmograph 12A (Wösthoff, Bochum, Germany), according to Bottner and Warembourg [1976]. Total N and ^{15}N were measured using coupled CHN/isotope mass spectrometry.
[9] Climatic parameters (daily precipitation, mean air temperature, and total radiation) were recorded using an automatic Campbell weather station at the site throughout the experiment period.
2.5. Predictive Models
[10] The five models tested with Vensim software (Ventana Systems, Inc., Harvard, Massachusetts) are presented in Figure 1. Three compartments are present in all the models: labile (VL), stable (VS) fractions of necromass (NC = VL + VL) and microbial biomass (MB). MOMOS3, 4, and 5 contain a compartment for humified compounds (H). MOMOS2 and 6 contain compartments for labile (HL) and stable (HS) humified compounds. MOMOS2 is the model already presented by Sallih and Pansu [1993] using data from a labeling experiment performed under laboratory conditions, with measurements of total ^{14}C, microbial biomass ^{14}C and not yet decomposed plant fragments ^{14}C. MOMOS3 results from the simplification of MOMOS2, with an equation system analogous to the RothC model [Jenkinson, 1990], but without the inert organic matter compartment of RothC (not necessary for this shortterm ^{14}C and ^{15}N experiment). MOMOS4 offers a further simplification of MOMOS3: The recycling part of H and MB compartments are removed. MOMOS5 explores two new modifications: (1) the whole outputs from plant material (VL+VS) and humus (H) compartments are the inputs of MB, and (2) the outputs of MB are defined by a respiration quotient (q_{CO2}) and a microbial mortality rate (k_{MB}). The equation system of MOMOS5 is similar to that of the CANDY model [Franko et al., 1995] and to that used by Saggar et al. [1996] to calculate ^{14}C turnover and residence times in soils. However, MOMOS5 differs from the former models in the following aspects: (1) fractionation of NC inputs into VL and VS, (2) change of kinetic calculation of the microbial respiration (see below, equations (9) and (10)), and (3) elimination of the flow fractionation between necromass and MB used in CANDY (in MOMOS5 the whole flow from the NC substrate enters into MB). MOMOS6 attempts to improve MOMOS5 by introducing a stable humus compartment (HS) that results from the slow maturation of HL and supplies the dormant MB with maintenance energy, when the fresh C input is exhausted. MOMOS5 and 6 are only regulated by firstorder kinetic constants (k parameters, dimension t^{−1}), without the dimensionless parameters (efficiency factors) often used in SOM models to fractionate the flows between the compartments (P parameters in MOMOS2 to 4, or, e.g., Jenkinson and Rayner [1977], Parton et al. [1987], or Franko et al. [1995]).
[11] For each model, the initial necromass (NC) was partitioned over VL and VR on the basis of its biochemical characteristics using the equations proposed by Thuriès et al. [2001, 2002], which give for this labeled straw the stable fraction of NC: f_{s} = 0.107.
[12] The general equation of the models is
where x is the vector of the state variables (compartments), is the vector of the rates variables, and A is the parameter matrix of each model. A and x are written, for MOMOS2,
for MOMOS3,
for MOMOS4,
for MOMOS5,
and for MOMOS6,
For the labeling experiment described in this paper (one single initial input of dead matter and an initial amount C_{0} of ^{14}C with a stable fraction f_{S}), the initial conditions are given by
[13] At each incubation time, the total ^{14}C evolution from the n compartments (n = 4 for MOMOS3, 4, 5; n = 5 for MOMOS2, 6) is given by
[14] In the case of MOMOS5 and 6, equation (8) becomes particularly simple,
where q_{CO2} is the metabolic quotient of the microbial biomass [Anderson and Domsch, 1993]. Another condition is necessary to ensure correct performance of MOMOS5 and 6: q_{CO2} must be controlled by the amount of MB. The q_{CO2} increases when MB is growing (particularly in response to the initial high supply from VL) and decreases when MB decreases or becomes inactive (dormant MB). Then is linked to MB by a secondorder kinetics. In order to allow use of MOMOS5 or 6 in different situations, we suggest (1) the introduction of a respiratory coefficient k_{resp} (dimension t^{−1}) and (2) the weighting of the k_{resp} values by the ratio of the actual level of MB in the studied soil and its equilibrium value (C_{MB}^{0} measured in biologically stable soil, i.e., a long time after the former inputs of substrate). For the present labeling experiment, C_{MB}^{0} = 0.15 g kg^{−1}, the level of MB^{14}C measured at the end of the experiment. The q_{CO2} is given by
[15] The N calculation of MOMOS2 to 6 is simplified compared to the initial MOMOSN model (MOMOS1 [Pansu et al., 1998]). Ammonia and nitrate pools are combined in a single pool of inorganicN. For each of the five models, the N state variables are derived from the C model, using the CtoN ratios of the compartments. If η is the vector of the CtoN ratios and y is the vector of N contents, the simulation of organic N status at a given incubation time is governed by
If η_{0} is the initial ^{14}Cto^{15}N ratio of the plant material, the inorganic ^{15}N (iN) is
In this labeling experiment, the values η_{0}, η_{t} (remaining total ^{14}Cto remaining total ^{15}N), and η_{MB} (^{14}Cto^{15}N of microbial biomass) were measured. The η_{VL} value is linked to η_{0} and η_{VS} by
The η_{H} or η_{HL} values are linked to the other data by
Thus the only η values that have to be estimated are η_{VS} (^{14}Cto^{15}N of the stable fraction of NC) in MOMOS3 to 5 or η_{VS} and η_{HS} (^{14}Cto^{15}N of the stable fraction of humus) in MOMOS2 and 6. In order to avoid irregularities in predictions, the values calculated for η_{H} or η_{HL} are smoothed in the interval [η_{MB}, (η_{0} + η_{MB})] with η_{HS} = 6 η_{MB}/5 for MOMOS6.
[16] During the simulations, the kinetic constants are daily corrected by two functions, one for temperature f(T) and one for moisture f(w); f(T) is a law with Q10 = 2 for a reference temperature of 20°C assumed to be valid for these mountain soils [Kätterer et al., 1998]; f(w) is a linear function of the actual soil moisture scaled by moisture content at field capacity (f (w) = 0 for w = 0). For the 5 to 10cm soil layer, the actual moisture was calculated by the SAHEL model [Penning de Vries et al., 1989]. With the corrective factor f(T) × f(w) in [0, 1] interval, the general formulation (equation (1)) of the models becomes
2.6. Comparison of the Predictive Quality and Sensitivity of the Models
[17] The four vectors of measured data were:
 −x_{t}
= total ^{14}C (nine sampling occasions (so) during 2 years of incubation), corresponding to the predicted values ,
 −y_{t}
= total ^{15}N (nine so) corresponding to the predicted values ,
 −x_{MB}
= MB^{14}C (nine so) corresponding to the predicted values _{MB},
 −y_{MB}
= MB^{15}N (nine so) corresponding to the predicted values _{MB},
For each model, four residual sums of square (RSS) were calculated for the m so,
[22] The smallest RSS corresponds to the best fit. In addition, the comparison should take the number of model parameters p into account. The best model has the smallest RSS and also the smallest p. MOMOS5 has five parameters: k_{VL}, k_{VS}, k_{MB}, k_{HL}, and k_{resp}. MOMOS3 and 4 have six parameters: k_{VL}, k_{VS}, k_{MB}, k_{H}, P_{MB}, and P_{H}. However, the specific parameterization of this experiment takes k_{VS} = k_{H} and reduces MOMOS3 and 4 to five parameter models. MOMOS2 has eight parameters: k_{VL}, k_{VS}, k_{HL}, k_{HS}, k_{MB}, P_{HL}, P_{MB}, and P_{HS}. However, again, the parameterization of this experiment takes k_{VL} = k_{HL}, k_{VS} = k_{HS}, and P_{HL} = 0.77 (value found by Sallih and Pansu [1993]) and also reduces MOMOS2 to a fiveparameter model.
[23] Thus the predictive quality of the models MOMOS2–5 can be pairwise compared by the F tests,
(u, t ∈ [2–5], t ≠ u, m sampling occasions, for each of the four models applied to each of the four series total^{14}C and ^{15}N, MB^{14}C, and ^{15}N.
[24] For a given state variable (SV), a scaled dimensionless sensitivity to a parameter (PA) can be defined by
for the SV total^{14}C, total^{15}N, MB^{14}C, and MB^{15}N from 13 November 1998 to 11 November 2000 at a daily time step. The values of the parameters were randomly sampled (200 simulations) from a normal distribution. For each parameter, the mean of the distribution is presented in Table 1; the relative standard deviation (sd) was 10%.
Table 1. Estimated Values of the Parameters for the Five Tested Models^{a}Model  Parameter Values 

k_{VL}  k_{VS}  k_{MB}  k_{HL}  k_{H}  k_{HS,}  k_{HLS}  k_{resp}  P_{MB}  P_{H}  P_{HS}  η_{VS}  η_{H}  η_{HS} 


MOMOS2  0.54  0.004  0.01  k_{VL}   k_{VS}    0.014   0.08  500   10.5 
MOMOS3  0.13  0.004  0.01   k_{VS}     0.06  0.36   450  10.9  
MOMOS4  0.13  0.002  0.007   k_{VS}     0.06  0.36   500  10.5  
MOMOS5  0.6  0.003  0.45   0.05    0.03     27  Cal  
MOMOS6  0.6  0.003  0.45  0.05   5 10^{−5}  3 10^{−4}  0.03     46  Cal  9.9 
SV  Sensitivity Analysis (S_{sv}, Equation (19)) of MOMOS4 (Type 1) Model 
k_{VL}  k_{VS}  k_{MB}  k_{HL}  k_{H}  k_{HS,}  k_{HLS}  k_{resp}  P_{MB}  P_{H}  P_{HS}  η_{VS}  η_{H}  η_{HS} 
Tot^{14}C 3 m  0.17  0.17  0.05   0.17     0.17  1.5     
Tot^{14}C 24 m  0.03  1.0  0.14   1.0     0.09  1.7     
Tot^{15}N 3 m  0.04  0.09  0.05   0.09     0.27  1.9     
Tot^{15}N 24 m  0.03  0.9  0.2   0.9     0.14  2     
MB^{14}C 3 m  0.17  0.08  0.3   0.08     2.5  0     
MB^{14}C 24 m  0.07  0.15  3.2   0.15     2.4  0     
MB^{15}N 3 m  0.16  0.07  0.2   0.07     2.4  0     
MB^{15}N 24 m  0.05  0.12  3.8   0.12     2.3  0     
SV  Sensitivity Analysis (S_{sv}, Equation (19)) of MOMOS6 (type 2) Model 
k_{VL}  k_{VS}  k_{MB}  k_{HL}  k_{H}  k_{HS,}  k_{HLS}  k_{resp}  P_{MB}  P_{H}  P_{HS}  η_{VS}  η_{H}  η_{HS} 
Tot^{14}C 3 m  0.3  0.02  1.2  0.5   <0.01  0.01  0.7       
Tot^{14}C 24 m  0.2  0.16  2.3  2.0   <0.01  0.16  1.1       
Tot^{15}N 3 m  0.4  0.02  1.2  0.5   <0.01  0.01  0.9       
Tot^{15}N 24 m  0.2  0.16  2.2  2.0   <0.01  0.2  1.2       
MB^{14}C 3 m  0.4  0.04  0.20  1.4   <0.01  0.02  1.1       
MB^{14}C 24 m  0.2  0.15  0.43  0.43   <0.01  0.09  1.5       
MB^{15}N 3 m  0.4  0.04  0.35  1.4   <0.01  0.02  1.1       
MB^{15}N 24 m  0.3  0.09  0.56  0.56   <0.01  0.06  1.5       