Modelling N mineralization from bovine manure and sewage sludge composts

Bioresource Technology 102 (2011) 863–871

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Modelling N mineralization from bovine manure and sewage sludge composts M.V. Gil, M.T. Carballo, L.F. Calvo ⇑ Chemical Engineering, Institute of Natural Resources, University of Leon, Avda. Portugal, 41, 24071 León, Spain

a r t i c l e

i n f o

Article history: Received 5 May 2010 Received in revised form 2 September 2010 Accepted 4 September 2010 Available online 15 September 2010 Keywords: Bovine manure Sewage sludge Compost N mineralization Kinetic models

a b s t r a c t Nitrogen mineralization kinetics were compared in three different soils (pH values: 5.2, 7.1 and 8.6) when treated with bovine manure (BM) and sewage sludge (SS) composts. The soil–compost mixtures were kept at a controlled moisture content of 60% of their water holding capacity (WHC) and were incubated in the dark at 25 °C for 2 years. Five mathematical models were compared (simple exponential, double exponential, special model, hyperbolic and parabolic), using as experimental data the mineralized N accumulated during 360 and 720 days of incubation. The results showed that the best fit for describing the mineralization of organic N from the compost after 1 year of experimentation was obtained with the simple exponential model. However, the special model showed the best fit for data from 2 years of incubation and thus better reflected organic N mineralization over a longer time-span. This suggested that the organic N in the two composts was made up of two organic pools of different degrees of stability. Ó 2010 Elsevier Ltd. All rights reserved.

1. Introduction The use of mathematical models to predict the amounts of nitrogen mineralized over time would allow the evaluation of soil’s capacity to supply N to plants and would make possible an assessment of the availability of mineral N in soils under different management options or with different properties (Pereira et al., 2005). Two main factors are of concern in relation to the study of the transformation of organic nitrogenous compounds in the soil. The first is the ‘‘potentially mineralizable N’’, or the maximum amount of inorganic N that can be formed. This depends upon mineralization and immobilization processes that are related to the ratio of carbon to nitrogen (C/N) in the organic matter, and also upon the type of organic material. The second factor of interest is the ‘‘rate of mineralization’’, which depends on soil and environmental conditions and the quality of organic matter. The environmental conditions that affect the mineralization process in soil are the moisture content, temperature (Wang et al., 2006), amount of oxygen and pH. It is important to quantify these factors as mathematical relationships which can be incorporated into more complex mathematical models relating to the N cycle in soil. With mathematical models, it is easier to evaluate the fate of N when organic fertilizers are applied to soils and to plan the optimum conditions for the use of nitrogen by plants. Empirical models are mathematical equations that can be fitted to the experimental results. The use of these models aims to evaluate or predict observed phenomena

⇑ Corresponding author. Tel.: +34 987 291844; fax: +34 987 291839. E-mail address: [email protected] (L.F. Calvo). 0960-8524/$ - see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.biortech.2010.09.010

or experimental data with the objective of developing adequate soil management practices. Models represent attempts at mathematical descriptions of a natural event. In respect of N mineralization, the main purpose of modelling is to obtain quantitative data to recommend the addition of N to the soil where appropriate (Camargo et al., 2002). However, modelling N dynamics in soils treated with organic wastes is difficult because of the transformation/turnover processes between the different pools of N in the soil (stable organic, degradable organic and inorganic N) and also because of the possible losses due to the high mobility of mineral N in the soil (Sistani et al., 2008). Moreover, availability of N from organic wastes varies according to the properties of the residue (Azeed and Van Averbeke, 2010) and the treatment process applied. Thus, composted materials gave lower mineralization rates than non-composted (Cordovil et al., 2007; Pansu and Thuriès, 2003; Tarrasón et al., 2008). In the same way, mature composts may mineralize in a shorter time period than fresh compost, since in fresh compost N-immobilization can occur (Amlinger et al., 2003). An evaluation of the availability of N in the soil can be carried out by means of short-term biological methods using incubation of samples in the laboratory. Under controlled conditions, this incubation provides the organisms linked to the conversion of organic N to ammonium with their optimum conditions for obtaining maximum mineralization rates. It also allows study of a soil’s N mineralization potential as a function of time (Pereira et al., 2005). Stanford and Smith (1972) suggested that each soil has an inherent potential to mineralize N under standard conditions. The estimation of the N mineralization parameters form field experiments can result difficult due to the high spatial variability in soils. However, laboratory incubation experiments provide the possibility of controlling

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environmental conditions and they can be valuable to understand the mineralization kinetics of organic materials added to soil, supplying useful information on short and medium term (Barral et al., 2009). Hernández et al. (2002) indicated that procedures for controlled incubation are the most satisfactory methods available for evaluating N availability. The incubation techniques can be carried out under different conditions, i.e., short-term or long-term; and with periodic lixiviation (leaching) or without lixiviation. However, in general, the assessment of N mineralization in static incubated soil samples is preferred to more laborious leaching procedures, which can underestimate N mineralization due to losses of soluble potentially mineralizable N in leachates (Smith et al., 1998). A number of equations have been used to model, and thus to describe, N mineralization kinetics in soils, although the rate of decomposition of organic materials in soil has been more commonly described by first-order kinetics. Mineralization is the process of decomposition of organic matter, mediated by soil microbes. Therefore, since microbial activity in soil is determined by enzyme dynamics, which are often described by an exponential equation, mineralization should theoretically be described with an exponential equation (Li et al., 2003). The model initially used to explain N mineralization dynamics in soil consisted of one first-order exponential equation (simple exponential model), proposed by Stanford and Smith (1972). These authors developed a laboratory procedure to investigate soil N mineralization, using a soil incubation experiment lasting 30 weeks with periodic lixiviation, under aerobic conditions and with controlled temperature and moisture. These authors used a first-order exponential equation to describe the data obtained when the accumulation of mineral N was analyzed as a function of time. On the basis of this equation, they defined the N mineralization potential as a pool of easily-mineralizable N in the soil which decomposes with a constant mineralization rate. In recent years, the incubation procedure developed by Stanford and Smith (1972) has been employed by other researchers in further investigations of soil N mineralization under controlled conditions in the laboratory (Cordovil et al., 2007; Dessureault-Rompré et al., 2010; O’Connell et al., 2003). Moreover, models with more than one component have been utilized to achieve a better analysis of experimental cumulative mineralized N as a function of time. A model with two components or two first-order exponential equations (double exponential model) was proposed by Molina et al. (1980) and Richter et al. (1980). It assumes that the two components represent two organic N fractions, one active and the other resistant, which decompose independently and simultaneously with different rate constants. Bonde and Rosswall (1987) modified the double model by replacing the resistant N pool with a constant term multiplied by time, thus proposing a mixed first- and zero-order exponential model (special model). These authors believed that in the light of the relative shortness of incubation compared to the half-life of the large resistant fraction of organic N, N mineralization from this resistant pool could appear to be linear rather than gradually declining. In the past few years, hyperbolic (Juma et al., 1984) and parabolic (Broadbent, 1986) models have also been proposed. The experiment reported here involved research into the organic N mineralization in three different soils, selected to include a range of pH values (acid, neutral and alkaline) from recently utilized residues, as composts. The objective of this work was to assess and compare the modelling of mineralization of organic N in three compost-treated soils. The composts used came from bovine manure and urban sewage sludge. The five mathematical models compared were: simple exponential, double exponential, special model, hyperbolic and parabolic. Of these, the model that gave the best description of organic N mineralization data was chosen.

2. Methods 2.1. Soils The three soils used were taken from the top 15–20 cm of three plots in the provinces of León and Valladolid, in northwest Spain, and were selected to include a range of pH values. Chemical properties of the soils at the beginning of the experiment are shown in Table 1. The selected soils principally differed in their pH value and organic matter content. In this way, they were named according to the pH value: acid, neutral and basic soils. Thus, the unamended soils were called Sa, Sn and Sb, respectively. The Sa, with a pH value of 5.23, was collected from a barley field in León Province which had not been cultivated for the previous 2 years. The Sn, with a pH value of 7.08, was collected from fallow land in León which had not been used to grow crops for the last 10 years. Finally, the Sb, with a pH value of 8.56, was taken from a plot without crops next to a vineyard in Valladolid. The soil texture was sandy clay loam in all these cases. Samples of approximately 50 kg were collected from each plot. The field-moist samples were brought to the laboratory, air-dried at room temperature for 48 h and passed through a 5 mm screen. They were then stored in a refrigerator at 4 °C until the moment that they were used. 2.2. Composts Two types of compost were studied: bovine manure (BM) compost and urban sewage sludge (SS) compost. The first compost used was produced from bovine manure (faeces and straw bedding) in the composting plant belonging to a livestock farm sited near the city of León in northwest Spain. The composting system used was the turned bed or channel, beds being covered with a roof and force-aerated from below. After the thermophilic stage, lasting about 2 weeks, the materials were placed in turned windrows, under a roof, during the maturation phase for an additional 8 weeks. The second compost used was produced from municipal sewage sludge in the composting plant belonging to the Municipal Wastewater Treatment Plant in Jerez de la Frontera in the Province of Cádiz in southwest Spain. In this plant, an activated sludge process is used to treat sewage. The compost was produced in a turned-pile system, mixing the anaerobic sewage sludge with green wastes. After approximately 2 months, when the bio-oxidative phase of composting was considered finished, the turning ceased to allow the compost to mature over a period of 2 months. Both composts were air-dried at room temperature and sieved (<5 mm mesh). Chemical properties of the composts are shown in Table 1. 2.3. Experimental setup A sample of soil (275 g air-dried and sieved soil) was treated with compost in order to reach an annual average fertilization equivalent of 220 kg per hectare (kg ha1) of N. The dosage of compost was determined by its N content, taking it into account that it released 15% of its organic N and 100% of its inorganic N (NH4+– N + NO3–N) annually (Bulluck et al., 2002). Moreover, we assumed that the soil released 2% of its organic N and 100% of its inorganic N (NH4+–N + NO3–N) annually. The amount of BM compost (on an oven-dried basis) applied was 44 tonnes per hectare (t ha1) in Sa (SaBM), 36 t ha1 in Sn (SnBM) and 29 t ha1 in Sb (SbBM). Likewise, the amount of SS compost (oven-dry basis) applied was 45 t ha1 in Sa (SaSS), 33 t ha1 in Sn (SnSS) and 29 t ha1 in Sb (SbSS). The control was a soil without compost (Sa, Sn and Sb). The soil and compost were mixed thoroughly. The soil–compost mixture was transferred to a cylindrical plastic pot (5.15 cm

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M.V. Gil et al. / Bioresource Technology 102 (2011) 863–871 Table 1 Properties of the soils and composts used in the experiment (means of three replicates ± standard deviations) (dry weight). Parameter

Sand (%) Silt (%) Clay (%) pH, H2O Organic matter (%) Kjeldahl N (g kg1) NH4+–N (mg kg1) NO3–N (mg kg1) C/N ratio

Soil

Compost

Acid (Sa)

Neutral (Sn)

Basic (Sb)

65.1 ± 2.2 10.0 ± 2.5 24.9 ± 1.0 5.23 ± 0.07 1.18 ± 0.16 0.73 ± 0.23 15.65 ± 0.89 0.75 ± 0.13

72.6 ± 1.1 6.9 ± 1.3 20.5 ± 1.8 7.08 ± 0.01 2.11 ± 0.10 1.17 ± 0.06 24.11 ± 0.82 7.96 ± 0.36

67.6 ± 2.1 9.2 ± 1.4 23.3 ± 0.7 8.56 ± 0.03 1.75 ± 0.18 1.25 ± 0.05 40.02 ± 3.96 11.62 ± 0.19

diameter and 18 cm length). All treatments were prepared in triplicate. Moreover, one sample was prepared for each day of sampling. In this way, a non-leached incubation experiment was prepared. The soil–compost mixtures were maintained at controlled moisture content, 60% of maximum water holding capacity (WHC), with distilled water, and aerobically incubated at 25 °C in the dark for 2 years. The corresponding samples were taken out of the incubator at 0, 20, 40, 60, 80, 120, 180, 240, 300, 360, 540 and 720 days after the beginning of the experiment. The soils were then analyzed for NH4+–N and NO3–N. Net mineralized N from soil organic N in each unamended soil (Sa, Sn and Sb) was calculated as the sum of the inorganic N forms in unamended soil minus the initial inorganic N in soil. Net mineralized N from compost in each amended soil (SaBM, SaSS, SnBM, SnSS, SbBM and SbSS) was calculated as the sum of the inorganic N forms in amended soil minus the net mineralized N from soil organic N of unamended soil and the initial inorganic N in soil and added compost, that is, it was calculated by subtracting the amount of mineralized N in the unamended soil from mineralized N in the compost-treated soil. 2.4. Chemical analyses The soil and compost samples were allowed to dry in the air and then ground and passed through a 2 mm mesh screen before analysis. Bouyoucos’ densimeter method was used to determine soil texture, which was obtained by fitting the percentages of sand, silt and clay fractions to the USDA soil texture classification triangle. The moisture content was determined by drying a sample at 105 °C until a constant weight was reached. Soil WHC was determined according to Sangnark and Noomhorm (2003). The pH was measured in 1:2.5 (m/v) soil/water ratio or 1:25 (m/v) compost/ water ratio. The organic matter (OM) content of the compost samples was analyzed by loss on ignition at 430 °C for 24 h (Navarro et al., 1993). Soil organic matter content was determined by the Walkley–Black wet digestion method. Total N concentrations were determined according to the Kjeldahl method. Ammonium–N concentrations were determined in KCl extracts using a pH ion-meter coupled with an ammonium ion selective electrode (APHA et al., 1989). Nitrate–N concentrations were determined in CaSO4 extracts using a UV–Vis spectrophotometer, in accordance with the method described by Sempere et al. (1993). 2.5. Models Five mathematical models were compared in this work, using as experimental data the mineralized N accumulated during the period of incubation. They are summarized in Table 2.The simple exponential model (Stanford and Smith, 1972) is defined by the following equation:

Nm ¼ N0 ½1  expðk0 tÞ

ð1Þ

Bovine manure (BM)

Sewage sludge (SS)

9.59 ± 0.01 43.28 ± 1.52 23.9 ± 5.5 126.7 ± 11.0 426.9 ± 55.1 10.9 ± 2.5

8.77 ± 0.08 21.88 ± 0.86 25.7 ± 0.6 104.3 ± 8.8 201.1 ± 20.9 5.0 ± 0.3

where Nm is the cumulative mineralized N (mg kg1) at time t (d), N0 is defined as the potentially mineralizable N (mg kg1) and k0 is the mineralization rate constant (d1).The double exponential model (Molina et al., 1980; Richter et al., 1980) is defined by this equation:

Nm ¼ Na ½1  expðka tÞ þ Nr ½1  expðkr tÞ

ð2Þ

where Na and ka represent, respectively, the potentially mineralizable N (mg kg1) and the mineralization rate constant (d1) of the active N fraction or easily available N pool and Nr and kr represent, respectively, the potentially mineralizable N (mg kg1) and the mineralization rate constant (d1) of the resistant N fraction. The sum of Na and Nr has the same physical meaning as the N0 in the equation for the simple exponential model (Deans et al., 1986).The special model (Bonde and Rosswall, 1987) is defined by the following equation:

Nm ¼ Na ½1  expðka tÞ þ V r t

ð3Þ

where Na and ka represent, respectively, the potentially mineralizable N (mg kg1) and the mineralization rate constant (d1) of the active N fraction or easily available N pool, whereas Vr is a constant that represents the mineralization rate of the resistant N fraction (mg kg1 d1). This constant is identified by the authors as the product of a large resistant N pool mineralizing at a low, constant rate.The hyperbolic model (Juma et al., 1984) is defined by the following equation:

Nm ¼ N0 t=ðbN0 þ tÞ

ð4Þ

where N0 is the potentially mineralizable N (mg kg1) and b is a constant (kg d mg1).The parabolic model proposed by Broadbent (1986) is the following:

Nm ¼ At b

ð5Þ

where A (mg kg1 d1) and b are constants. 2.6. Statistical analyses Data for the mineralized N accumulated were fitted to mathematical equations by the non-linear least-square curve-fitting technique (Marquardt–Levenberg algorithm), using SPSS v.14.0 software. The confidence intervals (95%) for the parameter estimates were selected in order to assess the statistical significance of curve-fitting. Furthermore, so as to compare the fits of different kinetics and identify the best model, the coefficient of determination (R2) and the residual mean of squares (RMS) were calculated. 3. Results and discussion Net mineralized N from compost organic N in the three soils studied, expressed as percentage of the organic N applied with the compost, is shown in Fig. 1. In the acid soil after the application

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Table 2 Mathematical models for estimating organic N mineralization in soils treated with compost. Model

Equation

Parameters

References

Simple exponential Double exponential Special model Hyperbolic Parabolic

Nm = N0 [1  exp(k0t)] Nm = Na [1  exp(kat)] + Nr [1  exp(krt)] Nm = Na [1  exp(kat)] + Vrt Nm = N0t/(bN0 + t) Nm = Atb

N0, k0 Na, ka, Nr, kr Na, ka, Vr N0, b A, b

Stanford and Smith (1972) Molina et al. (1980) and Richter et al. (1980) Bonde and Rosswall (1987) Juma et al. (1984) Broadbent (1986)

Nm: mineralized N at time t; N0: potentially mineralizable N; k0: mineralization rate constant; Na: potentially mineralizable N of the easily degradable organic nitrogen fraction; ka: mineralization rate constant of the easily degradable organic nitrogen fraction; Nr: potentially mineralizable N of the resistant organic nitrogen fraction; kr: mineralization rate constant of the resistant organic nitrogen fraction; Vr: mineralization rate of the resistant organic nitrogen fraction; b, A: constants.

Fig. 1. Net mineralized N from compost organic N in the three soils studied for both compost used, expressed as a percentage of the organic N applied with the compost.

of both composts (SaBM and SaSS) and in the basic soil after the application of bovine manure compost (SbBM), negative mineralization was observed during the early days of the experiment. In the SaBM and SaSS soils, the negative N mineralization is thought that is due to the existence of an immobilization process in the acid soil, since the organic N from compost increased during the first days of experiment (data not shown). However, it did not occur in the SbBM soil, being the negative N mineralization probably caused by N losses by ammonia volatilization in the basic soil. In the rest of treatments, the net mineralization of N was positive from the start of the experiment. Experimental data for mineralized N in compost-treated soils were fitted to five non-linear models used to predict nitrogen mineralization (Table 2). Data from 360 days into the experiment were first considered and thereafter the fit was repeated, taking into consideration all the data from the experiment (720 days), in order to check if the tendency in the N mineralization during the first year was different from the longer-term trend. For soils SaBM, SbBM and SaSS, which presented negative mineralization during the first few days of the experiment, the fit was carried out from the moment when mineralized N once again started to increase. Furthermore, the inclusion of a constant (C) in the model equation then proved necessary, representing the origin ordinate. Table 3 shows the results of the fits to the mineralized N data in BM treatments from the different models covering the data from the first 360 days, whilst Table 4 shows the results of the fits to the mineralized N data in SS treatments from the different models covering the data from the same period, the first 360 days. For each fit, the table shows the parameter estimates, the lower and upper

confidence interval limits (95%), the coefficient of determination (R2) and the residual mean of squares (RMS). If the confidence interval for one parameter does not include zero, this means that the parameter is significant. Therefore, for each treatment, the models whose parameters were all significant were selected as satisfactory. From these, the model with the highest R2 and the lowest RMS was chosen as the best model, this being underlined in the tables. After 360 days of experimentation, the data for N mineralization in the soils treated with compost in the case of all the treatments (Tables 3 and 4) best fitted to the simple exponential model proposed by Stanford and Smith (1972), since the fit was significant and this model presented the highest R2 and the lowest RMS among all the significant fits. None of the fits for the double exponential and special models relating to data from 360 days turned out to be significant, since the confidence interval for some of their parameters did include zero. The fit to the hyperbolic model was found significant except for SbBM and SaSS, and the fit to the parabolic model was found to be significant only for SnBM, SnSS and SbSS, although these presented lower R2 and higher RMS than the simple exponential model. This indicated that the consideration of more than one fraction of the organic N does not improve the fit. A higher value of R2 can be observed in other models than in the simple exponential model, but the parameter estimates were not significant, because their confidence interval included zero. Camargo et al. (2002) also concluded that the use of super-parametrized models, such as the double exponential, is not necessary to obtain an adequate fit to the N mineralization data. Table 5 shows the results of the fits to the mineralized N data in BM treatments of the different models, taking into consideration the data from 720 days, while Table 6 shows the results of the fits to the mineralized N data in SS treatments of these different models, likewise covering the data from 720 days of experimentation. In these tables, the best model has also been underlined. The fit to the N mineralization data after 720 days of the experiment (Tables 5 and 6) was different for soils SaBM and SbBM than in the remaining treatments. For soil SaBM, the model that presented the best fit after 720 days was the hyperbolic model, closely followed by the simple exponential model (Stanford and Smith, 1972), which was the best model with the data from 360 days of the experiment. The parabolic model also showed a significant fit, but less good than the others. The double exponential and special models presented a non-significant fit. For soil SbBM, none of the models considered fitted the N mineralization data significantly, these data being able to fit only a linear model, which showed a significant fit in this treatment. Benbi and Richter (2002) stated that N mineralization kinetics can be linear when a small fraction of organic N is slowly mineralized. For the remaining treatments, SnBM, SaSS, SnSS and SbSS, the model which presented the best fit to the N mineralization data after 720 days of experimentation was the special model (simple exponential + linear) proposed by Bonde and Rosswall (1987),

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Table 3 Results for the fit of mineralized N data in BM treatments to the different models: data from the first 360 days of the experiment (the underlined model was identified as the best model for each treatment). Treatment

SaBM

SnBM

SbBM

Model

Days considered

Simple exponential

80–360

Double exponential + constant

60–360

Special model + constant

80–360

Hyperbolic

80–360

Parabolic

80–360

Simple exponential

0–360

Double exponential

0–360

Special model

0–360

Hyperbolic

0–360

Parabolic

0–360

Simple exponential + constant

20–360

Double exponential + constant

20–360

Special model + constant

20–360

Hyperbolic + constant

20–360

Parabolic

40–360

Parameter

Estimate

Confidence interval 95% Lower limit

Upper limit

N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) C (mg kg1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) C (mg kg1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

123.00 0.0029 6822.47 0.0844 108.65 0.0033 –6819.90 119.30 0.0217 0.1348 –89.18 204.72 2.77 0.990 0.748

66.15 0.0009 7775.21 0.0457 82.86 0.0004 –21434.20 155.06 –0.0170 0.0442 –386.50 78.06 1.95 0.222 0.528

179.85 0.0048 21420.14 0.1230 135.45 0.0062 7794.40 393.66 0.0605 0.2254 208.14 331.37 3.58 2.202 0.968

N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

126.68 0.0051 431.93 0.0023 26933.03 –1.4E-05 436.63 0.0023 –0.3896 194.06 1.48 2.072 0.679

97.93 0.0029 130476.03 –0.2633 –9.0E+08 –0.4664 3805.02 –0.0110 –4.4620 127.05 1.06 0.016 0.498

155.43 0.0073 131339.89 0.2679 9.0E+08 0.4664 4678.28 0.0156 3.6829 261.08 1.90 4.128 0.860

N0 (mg kg1) k0 (d1) C (mg kg1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) C (mg kg1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) C (mg kg1) N0 (mg kg1) b (mg kg1) C (mg kg1) A (mg kg1 d1) b

33.20 0.0144 –16.00 38.92 0.0484 46836.11 9.4E-07 –34.64 38.92 0.0484 0.0441 –34.64 47.94 0.77 –25.75 0.155 0.832

19.35 0.0020 –31.15 17.54 –0.0875 –1.7E+09 –0.0334 –116.30 5.34 –0.0140 0.0162 –82.64 21.00 –0.90 –57.80 0.183 0.439

47.05 0.0268 –0.85 95.39 0.1842 1.7E+09 0.0334 47.02 83.19 0.1107 0.0720 13.37 74.88 2.44 6.30 0.492 1.224

since the fit was significant and this model presented the highest R2 and the lowest RMS among all the significant fits. The double exponential model once again showed a non-significant fit. In general, the simple exponential, hyperbolic and parabolic models presented significant fits but these were less good than those found with the special model. This may indicate that as N mineralization proceeds, mineralizable N resistance becomes greater and thus the rate of mineralization decreases. This also confirms the existence of two fractions of organic N with different degrees of degradability. Therefore, one part of the organic N would mineralize quickly, while most organic N would mineralize slowly and with a kinetic that is linear over time. Camargo et al. (2002) suggested that in order to test the hypothesis that there are two organic N pools, an incubation period of 1–2 years would be needed, and hence, it might possibly be that multiple exponential models would show some advantages over the single exponential models. In the experiment being reported here, the incubation period extended over 2 years, so the existence of two fractions of organic N was taken into account, since the fit

R2

RMS

0.9834

9.8

0.9999

0.5

0.9982

2.1

0.9818

10.8

0.9699

17.9

0.9808

34.2

0.9817

43.4

0.9817

37.2

0.9784

38.4

0.9581

74.6

0.9024

11.5

0.9668

5.9

0.9668

4.7

0.9311

8.1

0.8872

6.3

with the special model was better than the simple model when long-term data were considered. Benbi and Richter (2002) concluded that for a precise estimate of potentially mineralizable N, incubation needs to be continued until the mineralization rate appears to drop to a low and relatively constant value. It appears that the longer the incubation, the more precise are the parameter estimates. Dou et al. (1996) observed that the double and special models were better than the simple exponential and hyperbolic models. Li et al. (2003) also concluded that the special model gave the best model fit for N mineralization data in Chinese soils under aerobic and anaerobic conditions. On the other hand, Stanford and Smith (1972) obtained values for the mineralization rate constant of between 0.005 and 0.014 d1, Molina et al. (1980) of 0.014 d1 and Juma et al. (1984) of between 0.005 and 0.023 d1 for soil organic N using their respective mathematical models. Dossa et al. (2009) found values of the mineralization rate constant using the Stanford and Smith (1972) model of between 0.007 and 0.016 d1 for organic N in soil. In the same way, Sierra (2002) obtained values of

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Table 4 Results for the fit of mineralized N data in SS treatments to the different models: data from the first 360 days of the experiment (the underlined model was identified as the best model for each treatment). Treatment

SaSS

SnSS

SbSS

Model

Days considered

Simple exponential + constant

60–360

Double exponential + constant

60–360

Special model + constant

60–360

Hyperbolic + constant

80–360

Parabolic

80–360

Simple exponential

0–360

Double exponential

0–360

Special model

0–360

Hyperbolic

0–360

Parabolic

0–360

Simple exponential

0–360

Double exponential

0–360

Special model

0–360

Hyperbolic

0–360

Parabolic

0–360

Parameter

Estimate

Confidence interval 95%

R2

RMS

Lower limit

Upper limit

115.61 1.0127 –119.78 42.88 –0.0750 –2.3E+09 –0.5804 –517.27 95.34 0.0068 –0.0645 –168.72 15.56 0.52 1.825 0.226

178.87 0.0196 –53.33 259.23 0.1103 2.3E+09 0.5804 327.54 206.78 0.0284 0.0914 –21.02 275.82 4.83 4.136 1.161

0.9972

2.0

0.9974

3.7

Na (mg kg1) ka (d1) Vr (mg kg1 d1) C (mg kg1) N0 (mg k1) b (mg kg1) A (mg kg1 d1) b

147.24 0.0161 –86.55 151.06 0.0176 7336.08 1.8E-06 –94.87 151.06 0.0176 0.0134 –94.87 130.13 2.67 1.155 0.693

0.9974

2.5

0.8661

77.0

0.8257

100.2

N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

253.73 0.0082 257.21 0.0081 1452.98 –5.8E-06 257.24 0.0081 –0.0084 348.12 0.43 11.115 0.535

233.66 0.0066 1961.61 –0.0289 –6.6E+08 –2.5953 16.92 0.0012 –0.5792 298.55 0.34 3.052 0.401

273.80 0.0098 2476.03 0.0451 6.6E+08 2.5952 497.56 0.0150 0.5623 397.70 0.51 19.178 0.670

0.9920

68.4

0.9920

91.2

0.9920

78.1

0.9891

93.4

0.9615

331.1

N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

168.52 0.0094 141.07 0.0113 26278.20 2.8E-06 141.08 0.0113 0.0743 224.78 0.55 9.342 0.500

149.98 0.0068 825.62 –0.0348 –1.8E+09 –0.1951 10.30 –0.0002 –0.2925 184.29 0.39 1.742 0.349

187.05 0.0121 1107.75 0.0573 1.8E+09 0.1951 271.85 0.0227 0.4410 265.26 0.70 16.942 0.652

0.9798

81.1

0.9804

105.0

0.9804

90.0

0.9778

89.2

0.9456

218.2

N0 (mg kg1) k0 (d1) C (mg kg1) Na (mg kg1) Nr (mg kg1) kr (d1) C (mg kg1)

0.007–0.014 d1 for organic N in a tropical soil. Mungai and Motavalli (2006) found a value for the mineralization rate constant of 0.003–0.006 d1 for green wastes. Eghball (2000) obtained a value for the mineralization rate constant equal to 0.013 d1 for organic N from composted beef cattle feed-lot manure. Bernal et al. (1998) found a value equalling 0.083 d1 for sewage sludge compost. Hernández et al. (2002) obtained values between 0.033 and 0.163 d1 for organic N from sewage sludge applied to the soil. In this present study, involving bovine manure compost and sewage sludge compost, the mineralization rate constant was between 0.002 and 0.009 d1 approximately, a lower value than that found by other authors for animal wastes and even for organic N in soil. This could be due to the fact these composts were highly stable after the composting process, so that in this way they presented a slow mineralization of organic N. Comparisons of the model parameters for data relating to 360 and 720 days of incubation indicated that the estimated potentially mineralizable N, N0, increased in parallel with the incubation time, while at the same time the associated mineralization rate constant, k0, decreased. This was also observed by Juma et al. (1984). Some authors, such as Serna and Pomares (1992), suggested that the product N0k0, which represents the potential mineralization rate,

is a better indicator of N availability in soil than N0 alone. In the current work, that product, when the estimated parameters of the simple exponential model were taken into account, generally decreased between the 360-day and 720-day point. Moreover, N0k0 had the lowest value for soil SbBM, followed by soils SaBM and SaSS, and thereafter SnBM, SbSS and SnSS. Thus, it seems that a higher proportion of organic N from sewage sludge compost can be transformed to inorganic N, and at a higher mineralization rate, than from bovine manure compost. Furthermore, for both composts the potential mineralization rate proved to be higher in neutral soil than in acid and basic soils. On the other hand, fitting the double and special models to the mineralization data was sometimes impossible, or gave estimates for parameters that were meaningless values. Thus, the N0 or Na + Nr value was sometimes much greater than the compost’s organic N content and kr or Vr value was sometimes negative. This means that a mathematical calculation for two fractions of organic matter is not always possible, because the relationship of the calculated fractions to the pools existing in the compost is sometimes difficult to establish. Dendooven et al. (1997) stated that the hypothesis that the double exponential model characterizes the presence of two forms of organic N susceptible to mineralization

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Table 5 Results for the fit of mineralized N data in BM treatments to the different models: data from 720 days of the experiment (the underlined model was identified as the best model for each treatment). Treatment

SaBM

SnBM

SbBM

Model

Days considered

Parameter

Estimate

N0 (mg kg1) k0 (d1) Na (mg kg1) Nr (mg kg1) kr (d1)

Confidence interval 95% Lower limit

Upper limit

156.31 0.0020 48.18 0.0055 100980.74 1.03E-06 48.20 0.0055 0.1043 240.05 2.97 1.466 0.675

126.37 0.0014 650.86 –0.0377 –2.7E+09 –0.0274 5.10 –0.0014 0.0309 185.52 2.53 0.683 0587

186.25 0.0027 747.22 0.0488 2.7E+09 0.0275 101.50 0.0125 0.1776 294.63 3.40 2.248 0762

182.57 0.0028 61.02 0.0086 178966.02 8.09E-07

150.06 0.0019 89.29 –0.0078 –1.3E+09 –0.0057 26.77 0.0017 0.0861 205.61 1.42 1.156 0.540

215.09 0.0037 211.33 0.0251 1.3E+09 0.0057 95.31 0.0156 0.2034 317.97 2.10 4.084 0.726

R2

RMS

0.9888

14.5

0.9930

13.7

0.9930

10.9

0.9907

12.0

0.9872

16.5

0.9808

59.9

0.9893

41.7

0.9893

37.1

0.9846

48.1

0.9793

64.8

Simple exponential

80–720

Double exponential

80–720

Special model

80–720

Hyperbolic

80–720

Parabolic

80–720

Simple exponential

0–720

Double exponential

0–720

Special model

0–720

Hyperbolic

0–720

Parabolic

0–720

Linear Simple Exponential + constant

40–720

Slope (mg kg1 d1)

0.0628

0.0579

0.0678

0.9723

20–720

7.4

20–720

0.9818

6.3

Hyperbolic

40–720

0.9726

6.2

Parabolic

40–720

1837.17 0.0023 3.72 218.65 0.2323 6.4E+08 0.0008 116.58 189.52 0.2046 0.0711 85.96 4.1E+16 18.05 0.116 1.210

0.9818

Special model + constant

1329.99 –0.0017 –9.03 112.33 –0.0815 –6.4E+08 –0.0008 –221.05 83.22 –0.0538 0.0505 –190.42 4.1E+16 13.78 0.009 0.839

18.3

20–720

253.59 0.0003 –2.66 53.16 0.0754 223613.88 2.7E-07 –52.23 53.15 0.0754 0.0608 –52.23 2.7E+09 15.91 0.054 1.025

0.9398

Double exponential + constant

N0 (mg kg1) k0 (d1) C (mg kg1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) C (mg kg1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) C (mg kg1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

0.9726

6.2

Na (mg kg1) ka (d1) Vr (mg kg1 d1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

cannot be sustained or is sometimes excluded. These latter authors suggested that acceptable values could be obtained by restricting the range of variation for each of the parameters, such as limiting the size of the Nr fraction, in other words, reducing the amount of organic N added in the compost. However, these restrictions would be totally arbitrary. Furthermore, parameter estimates should not be considered exact quantitative values, since they depend on temperature and moisture conditions in the soil. However, they would be useful for detecting differences between soils and treatments in this experiment, since these were studied under identical conditions. In fact, models and their corresponding parameters are necessary for a mathematical description of soil or compost N mineralization kinetics. Many computer models simulating the N cycle in biological systems utilize such mathematical models and require the corresponding parameters. Estimated N0 values have been widely used as indices of the availability of organic N in soil for determining the effects on soil fertility of different agricultural practices, such as N fertilization management. In addition, the N0 value is an important input parameter required by many computer models simulating N cycling in soil–water–plant systems. On the other hand, Dou et al. (1996) pointed out that if parameter values

61.04 0.0086 0.1447 261.79 1.76 2.620 0.633

are taken from literature, care must be taken and factors such as the duration of incubation and the properties of residues should be considered. In addition, they suggested that, if possible, all the equation parameters should be taken from the same source, such as N0 and k0, because these two parameters have a reciprocal relationship. In any case, measured input parameters would always be more useful.

4. Conclusions The organic N mineralization data after 1 year of experimentation from both composts showed a best fit to the simple exponential model, whereas the data from 2 years showed a best fit to the special model. Therefore, as the experimental time increased from 1 to 2 years, the special model, with more parameters, proved more accurate than the simple exponential model in explaining the nitrogen mineralization kinetics in compost-amended soils. It indicated that organic N in compost consisted of two organic fractions with different degrees of stability: labile organic N, rapidly mineralizable in soil, and resistant organic N, slowly decomposed.

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Table 6 Results for the fit of mineralized N data in SS treatments to the different models: data from 720 days of the experiment (the underlined model was identified as the best model for each treatment). Treatment

SaSS

SnSS

SbSS

Model

Days considered

Simple exponential

60–720

Double exponential

60–720

Special model + constant

40–720

Hyperbolic + constant

60–720

Parabolic

60–720

Simple exponential

0–720

Double exponential

0–720

Special model

0–720

Hyperbolic

0–720

Parabolic

0–720

Simple exponential

0–720

Double exponential

0–720

Special model

0–720

Hyperbolic

0–720

Parabolic

0–720

Parameter

Estimate

Confidence interval 95% Lower limit

Upper limit

N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) C (mg kg1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

96.42 0.0034 60.54 0.0052 29480.51 1.4E-06 237.19 0.0297 0.0734 –199.02 136.69 2.76 2.075 0.581

70.40 0.0015 952.63 –0.0443 –1.6E+09 –0.0792 165.04 0.0222 0.0590 –273.94 83.68 1.64 0.475 0.376

122.43 0.0052 1073.71 0.0548 1.6E+09 0.0792 309.33 0.0372 0.0877 –124.09 189.70 3.87 4.625 0.785

N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) N0 (mg kg1) b (mg kg1) A (mg kg1 d1) b

267.18 0.0074 66183.56 1.1E-06 224.65 0.0092 224.67 0.0092 0.0723 333.01 0.41 19.893 0.415

253.62 0.0063 1.0E+09 –0.0171 11.92 0.0020 183.99 0.0067 0.0010 308.30 0.35 7.370 0.307

280.74 0.0084 1.0E+09 0.0171 437.38 0.0163 265.34 0.0116 0.1436 357.73 0.47 32.42 0.524

N0 (mg kg1) k0 (d1) Na (mg kg1) ka (d1) Nr (mg kg1) kr (d1) Na (mg kg1) ka (d1) Vr (mg kg1 d1) N0(mg kg1) b (mg kg1) A (mg kg1 d1) b

195.89 0.0068 126.01 0.0126 76841.00 1.6E-06 126.03 0.0126 0.1204 244.77 0.60 12.979 0.432

175.89 0.0049 2.10 0.0008 –4.1E+08 –0.0083 97.03 0.0075 0.0632 217.73 0.47 5.837 0.338

215.88 0.0087 249.91 0.0244 4.1E+08 0.0083 155.03 0.0177 0.1777 271.81 0.72 20.121 0.527

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0.9353

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82.3

0.9916

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70.3

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62.5

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84.0

0.9396

593.6

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159.6

0.9874

80.7

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71.7

0.9823

90.5

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226.1

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