Introduction

Sulfur (S) deficiencies in crops have become a worldwide problem in recent years (Eriksen 2009), and there is limited information on designing S fertilization plans as compared with other nutrients like nitrogen (N) and phosphorus (P). Soil sulfate concentration (SO4−2-S) at sowing (Sinitial) has been broadly used with varied success to predict S availability to crops (Van Biljon et al. 2004; Pagani and Echeverría 2011; Carciochi et al. 2016). These contrasting results can be partially explained by the unaccounted contribution of S through mineralization during the growing season (Eriksen et al. 1995).

Different methods have been proposed to study S mineralization. The long-term (≥ 10 weeks) aerobic incubation technique is considered the standard method to determine the S mineralization potential (S0). Although this technique has been widely used in many studies (Pirela and Tabatabai 1988; Ghani et al. 1991; Saviozzi et al. 2006; Boye et al. 2009), it is lengthy and laborious, and therefore unsuitable for soil testing laboratories. The use of a short-term (7 days) aerobic incubation (Smin-7d) has been proposed as an alternative to long-term incubations (Wyngaard and Cabrera 2015). Although Smin-7d was highly correlated with S0 (r = 0.85), this association was determined using only four soils (Wyngaard and Cabrera 2015).

Due to the close relationship between S and N microbial turnover in soil, it was suggested that S mineralization can be estimated from N mineralization (Tabatabai and Al-Khafaji 1980; Echeverría et al. 1996; Niknahad-Gharmakher et al. 2009). Among the methods to estimate N mineralization, the short-term (7 days) anaerobic incubation (Nan) has been widely used, as it is a fast, simple, and precise technique (Echeverria et al. 2000; Soon et al. 2007; Orcellet et al. 2017). In this regard, Wyngaard and Cabrera (2015) have proposed the use of Nan as a S0 predictor, since they have found a strong relationship between both variables.

Most S in soils (> 95%) is organic (Sorg) (Ghani et al. 1991). As Sorg is associated with soil organic C (SOC), many studies have correlated Sorg and/or SOC with S mineralization, observing a positive relationship (Riffaldi et al. 2006) or no relationship between these variables (Pirela and Tabatabai 1988; Eriksen et al. 1995). A possible explanation for these different results is that S mineralization does not depend on the size of the whole S organic pool (estimated by SOC or Sorg) but on the size of the easily mineralizable fraction. The lability of soil organic matter is inversely associated with the clay content, as fine particles protect organic matter from decomposition (Schnug and Haneklaus 1998; Six et al. 2002). Consequently, the SOC/clay and Sorg/clay ratios may improve the S mineralization estimation as compared with SOC and Sorg, respectively. Another alternative to account for the physical protection of organic matter is the one suggested by Cambardella and Elliott (1992). These authors proposed a particle size separation of soil into two fractions: the stable fraction associated with minerals (< 53 μm) and the labile particulate fraction (PF, > 53 μm). The S content in the PF (S-PF) was related to S mineralization (Wyngaard and Cabrera 2015), but this relationship needs to be validated as it was developed with a limited number of soils. The C content in the PF (C-PF) is associated with N mineralization potential (Domínguez et al. 2016). However, it has never been evaluated as a S mineralization index. In this sense, it is interesting to evaluate C-PF as a predictor of S mineralization for its simplicity and lower cost as compared with S-PF.

Plant S uptake (Suptake) is often used as a S mineralization estimation. Previous studies have related different chemical S extraction methods with Suptake by plants growing in pots (Scott 1981; Bansal et al. 1983; Eriksen 1997) or in field conditions (Blair et al. 1991). However, none of these studies related Suptake to S mineralization indexes.

The use of S mineralization indexes to determine S availability for crops is limited, as mineralization in the field does not only depend on the size of the mineralizable pool but on edaphic-climatic variables (texture, precipitations, temperature, among others). Thus, it is necessary to develop a model to predict S mineralization in field that considers all of these variables. The use of a simplified balance was proposed to calculate the apparent N mineralization in the field (Cabrera and Kissel 1988; Engels and Kuhlmann 1993; Egelkraut et al. 2003; Alvarez and Steinbach 2011). In the same way, the S balance method would allow calculating the apparent S mineralization (Smin-app) in unfertilized plots from the soil SO4−2-S content at sowing (Sinitial) and at crops physiological maturity (Sresidual), and the Suptake. However, so far, there are no reports of the use of a simplified balance to quantify S mineralization in field conditions.

Many studies evaluated S mineralization under laboratory conditions using long-term aerobic incubations (Pirela and Tabatabai 1988; Ghani et al. 1991; Saviozzi et al. 2006; Boye et al. 2009). However, only a few studies aimed to estimate the results from long-term incubations using simplified S mineralization indexes or soil properties (Niknahad-Gharmakher et al. 2009; Wyngaard and Cabrera 2015). Moreover, none of these studies associated long-term incubation results, S mineralization indexes, or soil properties with Suptake or Smin-app determined under field conditions. The development of simple predictors of S mineralization and its correlation with field-derived data can help improving S fertilization diagnosis based solely in Sinitial. Therefore, the objectives of this study were (1) to compare methods to estimate soil S mineralization, (2) to develop a model to predict soil S mineralization from S mineralization indexes and edaphic properties, and (3) to predict field-grown corn Suptake and Smin-app using different S mineralization indexes and edaphic-climatic variables as predictors.

Materials and methods

Soils

Twenty-six topsoil (0–20 cm) samples were taken in 2013 and 2014 from contrasting sites of the Argentinean Pampas (from 30.8° to 38.2° S and 57.1° to 61.8° W). Soil texture ranged from sandy loam to silt clay loam and SOC ranged from 10.3 to 46.1 g kg−1. Mean annual rainfall at the experimental sites was between 850 and 1000 mm, and average daily mean temperature was between 14.5 and 19 °C. Further description of the experimental sites is in Table 1. Soil samples were dried at 30 °C and ground to pass a 2-mm sieve for all analysis except for total S (St) and SOC, when a 0.5-mm sieve was used.

Table 1 Site location and soil characteristics (soil type, clay, and sand content, pH)
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Soil analyses

Soil properties

For all analytical techniques, three laboratory replications per sample were performed. The St determination was performed after a wet digestion with HNO3 and HClO4 (Zhao et al. 1994), and the extracted S was quantified by inductively coupled plasma emission spectrometry (ICP-AES) (Thermo Fisher 61E). The SO4−2-S concentration (Sinorg) was determined by ion chromatography on 0.01 M NH4Cl (1:10, soil:solution ratio) extracts (Maynard et al. 1987). Organic S was calculated by subtracting Sinorg from St. To determine SOC, a wet combustion method with maintenance of the oxidation reaction temperature (120 °C) for 90 min was performed (Schlichting et al. 1995). To separate the particulate fraction (PF), soil samples were dispersed and wet-sieved through a 53-μm sieve (Cambardella and Elliott 1992). Organic C content in the particulate fraction (C-PF) was quantified as previously explained for SOC, while S in the PF (S-PF) was measured as described for St.

Incubations

The long-term open incubation procedure was performed as described by Pirela and Tabatabai (1988). In detail, 20 g soil were mixed with 20 g of acid-washed sand and transferred into a leaching tube with glass wool at the bottom. The soil-sand mixture was leached with 200 mL of 0.01 M CaCl2 to remove the initial sulfate. Then, excess water was removed by vacuum suction at 6 kPa, and samples were covered with a porous plastic film (PARAFILM®, Menasha, WI) and incubated at 30 °C and at a water content of 80% of field capacity. Soil moisture was corrected gravimetrically every 3 days and samples were leached with 0.01 M CaCl2 every 2 weeks for a 10-week period. Sulfate concentration in the leachate was measured by ion chromatography (Met Rohm IC 820 separation system, 819 conductivity detector with carbonate and cation suppression).

To describe soil S mineralization, data from the long-term open incubation technique were fitted to the following models based on previous studies (Zhou et al. 1999; Riffaldi et al. 2006; Saviozzi et al. 2006):

$$ \mathrm{First}-\mathrm{order}\ \mathrm{model}:{\mathrm{S}}_{\mathrm{m}}={\mathrm{S}}_{\mathrm{o}}\ \left(1-\exp \left(-{\mathrm{k}}_{\mathrm{F}}\mathrm{t}\right)\right) $$
$$ \mathrm{Zero}-\mathrm{order}\ \mathrm{model}:{\mathrm{S}}_{\mathrm{m}}={\mathrm{k}}_{\mathrm{Z}}\mathrm{t}+\mathrm{intercept} $$

where Sm is the cumulative S mineralized (mg kg−1) at a specific time (t) (week); S0 is the potentially mineralizable S (mg kg−1); kF is the first-order rate constant (week−1); and kZ the zero-order rate constant (mg S kg−1 week−1).

The Smin-7d determination was performed as proposed by Keeney and Bremner (1962). A 10-g soil sample was mixed with 30 g of acid-washed sand and transferred to a 50-mL plastic tube. After this, samples were moistened to 80% of field capacity water content, covered with a porous plastic film (PARAFILM®, Menasha, WI), and incubated for 7 days at 40 °C. Water content was corrected gravimetrically every 3 days. After the incubation period, SO4−2-S was extracted with 0.01 M NH4Cl at a 10:1 solution/soil ratio (Maynard et al. 1987) and quantified by ion chromatography. To obtain the Smin-7d, the initial SO4−2-S concentration (Sinorg) was subtracted from the final value (Smin-7d + Sinorg).

Finally, to determine Nan, a short-term anaerobic incubation was performed. The NH4+ produced after the incubation of 10 g soil saturated with distilled water at 40 °C for 7 days (Keeney 1982) was quantified by steam micro-distillation (Bremner and Keeney 1965).

Field experiments

In 2013 and 2014, field experiments were carried out in 18 out of the 26 experimental sites. The objective of these experiments was to determine S uptake by corn aerial biomass (Suptake) and the apparent S mineralization (Smin-app). Three replications were performed at each site, and the size of each plot was 12 by 5 m. Corn was sown at a 60,000 to 80,000 plant ha−1 density, depending on the site. All experiments were fertilized with N (200 kg N ha−1) as urea (46 g N 100 g−1) and P (30 kg P ha−1) as triple superphosphate (20 g P 100 g−1), but no S fertilizer was applied. All experiments were performed under no tillage, without irrigation, and in soils with deep groundwater tables (below rooting zone). When necessary, weeds were controlled by glyphosate [N-(phosphonomethyl)glycine] application at a 1.44 kg a.i. ha−1 rate. Rainfall and average daily mean temperature data during corn growing season were obtained from research meteorological stations located in or near the experimental sites.

At corn sowing and physiological maturity, composite soil samples (eight subsamples per plot) were taken at 0–20, 20–40, and 40–60 cm depths. Samples were dried at 30 °C and ground to pass a 2-mm sieve. Soil SO4−2-S concentration was determined as described in the soil analysis section. The bulk density of each site, estimated as proposed by Hollis et al. (2012), was used to convert SO4−2-S concentrations from milligrams per kilogram to kilogram per hectare.

At physiological maturity, ten plants were cut at ground level and dried at 60 °C. Plant samples were weighed and ground. Plant S concentration was measured by dry combustion at 1350 °C and thermoconductivity detection with TruSpec S analyzer (LECO, St. Joseph,MI, USA). Plant density was determined in each site to calculate Suptake (kg S ha−1).

The simplified balance method applied for N by Alvarez and Steinbach (2011) was used to determine the apparent S mineralization (Smin-app):

$$ {\mathrm{S}}_{\min \hbox{-} \mathrm{app}}={\mathrm{S}}_{\mathrm{uptake}}+{\mathrm{S}}_{\mathrm{residual}}-{\mathrm{S}}_{\mathrm{initial}} $$

where Smin-app (kg ha−1) represents the difference between net S mineralization and S losses from soil-plant system; Suptake the amount of S (kg ha−1) accumulated in corn aerial biomass at physiological maturity; Sresidual and Sinitial the SO4−2-S content (kg ha−1) in soil at 0–60 cm depth in physiological maturity and sowing, respectively.

As Smin-app does not consider S losses, we aimed to improve the S field balance by accounting for this last process. To do so, we weighted Sinitial by an uptake efficiency factor analogous to the one used in field N balances (Meisinger 1984). We used uptake efficiency values described for N, as there are no reports of Sinitial efficiency in literature. For N, initial NO3− uptake efficiency is described to range between 35 and 70% depending on precipitations (Meisinger et al. 2008). As S leaching (Sleaching) is the main process by which Sinitial is lost from the system (Schoenau and Malhi 2008), we considered rainfall from sowing to V6 stage when assigning an uptake efficiency to each site: a 35% S uptake efficiency was assigned to the site with greater rainfall (141 mm), while a 70% value was assigned to the site with lower rainfall (5 mm). A Sinitial uptake efficiency between 35 and 70% proportional to the precipitations between sowing and V6 was assigned to the rest of the sites. We named this new balance Smin-app (modified):

$$ {\mathrm{S}}_{\min \hbox{-} \mathrm{app}\ \left(\mathrm{modified}\right)}={\mathrm{S}}_{\mathrm{uptake}}+{\mathrm{S}}_{\mathrm{residual}}-{{\mathrm{S}}_{\mathrm{initial}}}^{\ast }\ \mathrm{Uptake}\ \mathrm{efficiency} $$

Statistical analysis

Zero- and first-order models for S mineralization were fitted using the R software (R Core Team 2017). Difference between sites for some variables was analyzed using the ANOVA procedure included in the R software (R Core Team 2017). Significantly, different means were compared using a LSD test at p = 0.05. Correlations between some variables were determined using the cor.test procedure included in the R software (R Core Team 2017). The stepwise selection method, included in the R software, was used to determine the best variables combinations to explain Smin-10wk, Smin-app, and Smin-app (modified) using a maximum p value of 0.05. Linear models to predict Smin-app and Smin-app (modified) were fitted using the lm procedure included in the R software (R Core Team 2017). The relationship between Suptake and some variables was described with linear-plateau models: y = a + b * x if x ≤ c and y = a + b * c if x > c, where a is the intercept, b is the slope during the linear phase, and c is the value of x at which the linear model reaches a plateau.

Results and discussion

Soil properties and S mineralization indexes

Some soil characteristics and S mineralization indexes are shown in Table 2. Total S content (St) was 487 ± 157 mg kg−1 and organic S (Sorg) was in average a 98.6% of St. Similar values of St were reported by Tabatabai and Al-Khafaji (1980), Boye et al. (2009), and Niknahad-Gharmakher et al. (2009) for arable soils from Iowa, Sweden, and France, respectively, where SOC content was similar to that in our study (between 10.3 and 46.1 g kg−1). The SOC/Sorg ratios ranged from 28.6 to 75 and are within the reported range (Pirela and Tabatabai 1988; Riffaldi et al. 2006; Niknahad-Gharmakher et al. 2009). Organic C in the PF and S-PF ranged around 3.2 g kg−1 and 97.2 mg kg−1 in average, respectively.

Table 2 Some soil properties and S mineralization indexes (mean ± SD; n = 3)
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The Smin-7d ranged from 0.2 to 3 mg kg−1. When the initial inorganic S was not subtracted, (Smin-7d + Sinorg) ranged from 1.3 to 10 mg kg−1. In average, Smin-7d represented 0.2% of Sorg, while Smin-10wk represented 1.1%. We observed a great variability between laboratory replications in the Smin-7d technique (avg. 56.3%; Table 2). This great variability is probably a consequence of the difficulty of adjusting contrasting samples to a water content of 80% of field capacity. The Nan ranged between 19.3 and 159.6 mg kg−1, and this range is within the one reported for agricultural soils in the same area by Reussi Calvo et al. (2013) and Orcellet et al. (2017).

Long-term S mineralization incubation

Mineralizable S determined by long-term (10 weeks) aerobic incubation (Smin-10wk) ranged between 2.2 and 12.8 mg kg−1 (Table 3). These values were in line with those determined in similar soils from Argentina (Echeverría et al. 1996), and in other soils from Chile (Pirela and Tabatabai 1988), France (Niknahad-Gharmakher et al. 2009), and the USA (Wyngaard and Cabrera 2015).

Table 3 Parameters, determination coefficients (R2) for first- and zero-order models and cumulative S mineralized after 10 weeks aerobic incubation (Smin-10wk) (mean ± SD; n = 3)
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To describe S mineralization kinetics, zero- and first-order models were fitted. The R2 values were high for both models, ranging from 0.93 to 0.99 for zero-order models and from 0.95 to 1.00 for first-order models (Table 3). Although the first-order model fits well for all the soils, the resulting S0 values were very high (> 92 mg kg−1) and unrealistic for 8 out of 26 soils where the zero-order model fitted better. In these eight soils, S0 represents between 25 and 97% of St, whereas this value is generally described to be lower than 15% (Pirela and Tabatabai 1988; Saviozzi et al. 2006; Wyngaard and Cabrera 2015). Similar results were reported by Pirela and Tabatabai (1988), Tabatabai and Chae (1991) and Zhou et al. (1999) who could not fit the first-order model or obtained unrealistic S0 values for some of the studied soils. Examples of these contrasting relationships between cumulative S mineralized and incubation time are shown in Fig. 1. For some soils, the rate of S release decreased with time, showing a curvilinear relationship (Fig. 1a), while in other soils this relationship was linear (Fig. 1b). Similar results were reported by Pirela and Tabatabai (1988) and Saviozzi et al. (2006), who observed that some soils presented a linear fit while others presented a quadratic fit. This may be a consequence of the different size of the easily mineralizable pool between soils: soils with a greater labile pool producing a mineralization flush during the first incubation weeks which results in a quadratic fit (Saviozzi et al. 2006). Meanwhile, Tabatabai and Al-Khafaji (1980) and Boye et al. (2009) described that cumulative amounts of S mineralized were linear with time, while other authors reported a decreasing rate of S release over time (Echeverría et al. 1996; Zhou et al. 1999; Saviozzi et al. 2006).

Fig. 1
figure 1

Examples of different relationships between S mineralized and time of incubation: a soils with curvilinear relationship and b soils with linear relationship. Vertical bars represent the standard deviation among replications

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The first-order rate constant kF varied between 0.008 and 0.197 week−1 without considering the eight soils with a high S0, where the kF was lower than 0.004 week−1 (Table 3). Similar rates of mineralization kF were also reported by Pirela and Tabatabai (1988), Tabatabai and Chae (1991), and Zhou et al. (1999), but our results are lower than those reported by Riffaldi et al. (2006) and Saviozzi et al. (2006). The product of S0 and kF (S0kF), which is called the initial potential rate of S mineralization, was used by Riffaldi et al. (2006) and Saviozzi et al. (2006) to estimate S mineralization. This product is described to be a better predictor of S mineralization than S0 and kF, as it considers the interdependence between these two variables. In our study, high S0 values result from low kF values. Therefore, the product between these two variables would help fixing the problem of great S0 values.

For the zero-order model, the slope kZ varied between 0.23 and 1.12 mg S kg−1 week−1 (Table 3). Our results were similar to those reported by Niknahad-Gharmakher et al. (2009) and Pirela and Tabatabai (1988) for agricultural soils, but were lower than those reported by Tabatabai and Al-Khafaji (1980), who reported an average kZ value of 2.5 mg kg−1 week−1 for pasture soils.

Correlation between S mineralization indexes

Table 4 shows the Pearson correlation coefficients (r) between different S mineralization indexes. The S0 estimated from first-order models was not correlated with any of the analyzed variables. This is due to the lack of fit of the data to a first-order model in some soils. For these data points, a zero-order model fitted better (Table 3). Moreover, kZ correlated better with Smin-10wk than kF did (r = 1 vs. r = 0.8, Table 4), indicating that S mineralization kinetics in the soils we analyzed evolved predominantly linear with time. Because of this, we decided to use Smin-10wk as a reference S mineralization capacity value instead of S0. Although S0 was not related with Smin-10wk, the S0kF product was highly correlated with Smin-10wk (r = 0.93). This finding contradicts the results from Riffaldi et al. (2006) and Saviozzi et al. (2006), who did not find significant correlations between S0kF and S mineralization indexes but agrees with results reported for N (Campbell et al. 1991; Burket and Dick 1998) and C mineralization (Riffaldi et al. 1996).

Table 4 Pearson correlation coefficients and significance between different S mineralization indexes
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The Smin-10wk correlated with all indexes except with the Sorg/clay ratio and S-PF, which were not related to any of the evaluated variables. Clay interaction with SOC or Sorg is described to be the major mechanism protecting S organic pools from microbial breakdown, as sulfate ester (the most labile form of Sorg) concentration increases with decreasing particle size (Schnug and Haneklaus 1998). However, SOC/clay and Sorg/clay ratios did not improve the capacity of SOC and Sorg of predicting Smin-10wk (r = 0.85 vs. r = 0.80 and r = 0.68 vs. r = 0.19 for SOC vs. SOC/clay and Sorg vs. Sorg/clay, respectively; Table 4). Therefore, the mere division of the organic pools by soil texture (SOC/clay and Sorg/clay) was inadequate to account for the capacity of soils to protect organic compounds from microbiological mineralization.

The C-PF and S-PF have been proposed as indexes to quantify the size of labile organic C and S pools (Galantini and Rosell 1997; Haynes 2005). Therefore, we expected C-PF and S-PF to be better predictors of S mineralization than SOC and Sorg, respectively. However, in our study this only occurred for C, as C-PF was slightly better correlated with Smin-10wk than SOC (r = 0.89 vs. r = 0.85 for C-PF and SOC, respectively; Table 4). This is the first time C-PF is evaluated as an index to predict S mineralization, although it had already been used to predict N mineralization (Domínguez et al. 2016). On the other hand, Smin-10wk was correlated with Sorg (r = 0.68) but not with S-PF (Table 4). Different results were reported by Wyngaard and Cabrera (2015) who found significant correlations between S0 and Sorg (r = 0.87) and S-PF (r = 0.84). A possible explanation for these contrasting results is that Wyngaard and Cabrera (2015) worked with only four soils, but with very contrasting edaphic properties. Results from other studies suggest that soils with high SOC content generally mineralize large amounts of S (Searle 1992; Riffaldi et al. 2006; Saviozzi et al. 2006), particularly those with low SOC/Sorg ratio (Kowalenko and Lowe 1975). Along this line, we found a positive correlation between SOC/Sorg ratio and Smin-10wk (r = 0.79; Table 4).

Comparing between incubation indexes, Smin-7d correlated well with Smin-10wk (r = 0.73; Table 4), but this correlation was improved when Sinorg was not subtracted from the SO4−2-S concentration determined after incubation (Smin-7d + Sinorg) (r = 0.89; Table 4). The fact that Sinorg improved Smin-7d performance as a S mineralization predictor can be explained by the positive relationship between Sinorg and Smin-10wk (r = 0.83; Table 4), which has been described before by Searle (1992), Reddy et al. (2001), and Niknahad-Gharmakher et al. (2009). The association between Smin-10wk and Sinorg can result from the accumulation of mineralized Sinorg before soil sampling and/or during the air-drying process (Williams 1967; Tabatabai and Bremner 1972; Ghani et al. 1991). Therefore, when the Sinorg released by mineralization is accumulated and not lost from the soil, it can help estimating its S mineralization potential. The use of Smin-7d + Sinorg does not only improve the predictive capacity but simplifies the technique as compared with Smin-7d.

Finally, Nan was highly correlated with Smin-10wk (r = 0.88, Table 4), confirming that methods to estimate N mineralization can be used to estimate S mineralization. Moreover, Nan cannot only be used to diagnose S availability to crops (Carciochi et al. 2016) but also N availability, as was reported by other authors (Reussi Calvo et al. 2013; Orcellet et al. 2017).

Models to predict S mineralization

Two models for predicting Smin-10wk from soil properties and S mineralization indexes resulted from the stepwise procedure. Both models included SOC, C-PF, and data from an incubation method (Smin-7d + Sinorg for model 1 and Nan for model 2) (Table 5). The SOC and C-PF account for the total and labile organic pool, respectively, which are the sources for microbiological S mineralization (Scherer 2001), while incubation indexes account for the microbial degradation of the organic pool (Scherer 2001). Between the two proposed models, we suggest the use of model 2, as it uses Nan instead of Smin-7d + Sinorg. This is because the determination of Nan is based on an easier technique and it has shown a 10-times lower variability between replicates than Smin-7d + Sinorg (Table 2). A third model was proposed as a simplified version of model 2 (Table 5) without considering C-PF, which did not generate a great contribution to the predictive capacity of the model. Thus, the simplified model had a little lower adjusted coefficient of determination than model 2 (Ra2 = 0.87 vs. 0.89, for models 3 and 2, respectively). Similarly, Niknahad-Gharmakher et al. (2009) generated an equation to predict S mineralization that included SOC, but unlike our model, it also accounted for pH, Sinorg, and clay content as predictive variables. The inclusion of soil pH is probably a consequence of the alkaline calcareous soils used in the latter study (average pH = 7.8). Even though our model included less variables than the one proposed by Niknahad-Gharmakher et al. (2009), it had a greater predictive capacity (Ra2 = 0.87 vs. 0.84).

Table 5 Models to predict Smin-10wk with different soil variables and S mineralization indexes: soil organic carbon (SOC), particulate organic carbon (C-PF); mineralizable S determined by short-term aerobic incubation + SO4−2-S before incubation (Smin-7d + Sinorg), and mineralizable N determined by short-term anaerobic incubation (Nan)
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Prediction of corn S uptake

Rainfall during corn growing season ranged from 422 to 721 mm depending on site (Table 6). At sites S1, S17, and S18, total rainfall was lower than corn water demand (around 550 mm) (Table 6), which may have limited corn growth. The average daily mean temperature was similar to the historical record for each site and did not negatively affect crop growth (data not shown).

Table 6 Edaphic and climatic properties at 18 cornfield experimental sites including: rainfall during corn growing season (total) and from sowing to V6 stage, average daily mean temperature during corn growing season, SO4−2-S content 0–60 cm depth at sowing (Sinitial), and Sinitial affected by an uptake efficiency (Sinitial (modified)), SO4−2-S content 0–60 cm depth at physiological maturity (Sresidual), S uptake in aerial biomass (Suptake), apparent S mineralization (Smin-app), and Smin-app accounting Sinitial (modified) (Smin-app (modified)) (mean ± SD; n = 3)
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Sulfur uptake (Suptake) in aerial biomass by corn is shown for the 18 experimental sites (Table 6). The Suptake ranged from 10.6 to 24.2 kg S ha−1. These values agree with those reported by Pagani et al. (2012) for the same region. The Smin-app varied between 3.2 and 29.4 kg ha−1 during the corn growing period, while Smin-app (modified) varied from 10.0 to 40.5 kg ha−1 (Table 6). These values agree with the S mineralization values reported by Bloem (1998) (10 to 30 kg ha−1 year−1) in soils with similar SOC content as those in our study. Additionally, Smin-app (modified) represented 1 to 4% of Sorg, in accordance with the values reported by Freney (1986) and Eriksen et al. (1998).

Linear-plateau relationships between Suptake and S mineralization indexes were observed (Fig. 2). The Smin-10wk had a good predictive capacity of Suptake (R2 = 0.73, Fig. 2), proving that S mineralization determined by laboratory incubations is related to S mineralization in the field, since this process is the main source of plant available S in unfertilized plots. The Suptake was also associated with S0kF (R2 = 0.76; Fig. 2), as with some S mineralization indexes (C-PF, Nan, Smin-7d + Sinorg, and Sinorg) (Fig. 2). The threshold values above which maximum Suptake was reached were 2.8 g kg−1, 59 mg kg−1, 3.1 mg kg−1, and 2.7 mg kg−1 for C-PF, Nan, Smin-7d + Sinorg and Sinorg, respectively (Fig. 2). Remarkably, previous studies have reported a relationship between Suptake and Sinorg for different crops (Scott 1981; Bansal et al. 1983; Eriksen 1997), but none of them related Suptake with S mineralization indexes.

Fig. 2
figure 2

Linear-plateau models to describe the relationship between S uptake in corn aerial biomass (Suptake) and a S mineralized after 10 weeks aerobic incubation (Smin-10wk), b initial potential rate of S mineralization (S0kF), c organic C in the particulate fraction (C-PF), d N mineralized in anaerobic incubation (Nan), e the sum of S mineralized after 7 days aerobic incubation and initial SO4−2-S (Smin-7d + Sinorg), and f initial SO4−2-S (Sinorg). CI is the confidence interval of the critical threshold (0.95). p indicates significance of regression

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Prediction of Smin-app and Smin-app (modified)

The stepwise procedure was used to determine a model to predict Smin-app (model 4). Although a significant model was generated, which included C-PF and SOC/clay, it presented a weak predictive capacity (R2 = 0.35). When one variable was considered, C-PF was the only index that was associated with Smin-app (model 5), but with a very low determination coefficient (R2 = 0.24).

  • Model 4. Smin-app = 4.43 * C-PF − 10.58 * SOC/clay + 11.71; R2 = 0.35; p = 0.016.

  • Model 5. Smin-app = 2.45 * C-PF + 5.64; R2 = 0.24; p = 0.038.

The low predictive capacity of S mineralization indexes for Smin-app is probably a consequence of Smin-app being determined using a simplified balance which does not take into account potential S losses during the crop cycle. Considering that leaching is the main loss process in S cycling (Schoenau and Malhi 2008), in those sites with significant S losses, Smin-app would underestimate S mineralization. To partially solve this problem, Smin-app (modified) was calculated using an efficiency for Sinitial uptake. Thus, the C-PF (model 6) explained 62% of Smin-app (modified) variation.

The importance of considering S leaching is observed when comparing models 5 (simplified balance) and 6 (considering Sinitial uptake efficiency). Moreover, it is likely that Smin-app (modified) estimation would be improved by increasing the soil sampling depth below 60 cm, as SO4−2-S content in subsurface soil is variable between sites and represents an important source of S availability (Haneklaus et al. 2007). Strangely, temperature was not selected as a variable to predict Smin-app or Smin-app (modified). This climatic variable is an important factor affecting S mineralization (Eriksen 2009; Schoenau and Malhi 2008) and is usually considered in models to predict N mineralization in the field (Cabrera and Kissel 1988; Egelkraut et al. 2003; Alvarez and Steinbach 2011). However, as the S mineralizable pool size is governed by the temperature of each site (Wang et al. 2006), this variable was indirectly considered. Also, it must be considered that the narrow temperature range between sites in our study (5 °C) (Table 6) may have limited the explicative capacity of temperature over Smin-app or Smin-app (modified). Finally, Smin-10wk was also associated with Smin-app (modified) (model 7) confirming the relationship between S mineralization in laboratory and in field conditions.

  • Model 6. Smin-app (modified) = 4.65 * C-PF + 9.86; R2 = 0.62; p < 0.001.

  • Model 7. Smin-app (modified) = 3.0 * Smin-10wk + 7.4; R2 = 0.54; p < 0.001.

Finally, it must be considered that S mineralization is a process mediated by microorganisms. Therefore, S mineralization should not only depend on the composition and protection of the mineralizable pool but also on the composition and activity of the microbial community. The importance of these last two microbial variables has been determined in other S cycling processes: recently, Zhao et al. (2017) demonstrated that the abundance and diversity of S-oxidizing bacteria are associated with the oxidation rate of elemental S. In our study, we focused on using edaphic-climatic data to estimate S mineralization (Smin-10wk, Suptake, Smin-app, and Smin-app (modified)). However, in future studies, it would be important to analyze the effect of the abundance and diversity of S-mineralizing bacteria on S mineralization under field conditions.

Conclusions

We determined that short and easily measurable indexes as Smin-7d + Sinorg, C-PF, SOC, and Nan can be used to model S mineralization measured by the standard long-term incubation method. Some of these indexes were also associated with Suptake by corn growing under field conditions, suggesting that they can be potentially used as S diagnostic methods. We also evaluated the unprecedented use of a simplified S balance to determine Smin-app. However, the S mineralization indexes failed to predict Smin-app, probably because this balance does not consider Sinitial losses. This inconvenience was overcome by developing a new balance accounting for the effect of precipitations over Sinitial efficiency uptake. Although further studies are necessary to validate the proposed models, they represent a significant advance in predicting S availability to crops under field conditions.