Geoderma 261 (2016) 204–221 Contents lists available at ScienceDirect Geoderma journal homepage: www.elsevier.com/locate/geoderma Digital mapping of soil carbon in a viticultural region of Southern Brazil Benito R. Bonfatti a,b,c, Alfred E. Hartemink b,⁎, Elvio Giasson a, Carlos G. Tornquist a, Kabindra Adhikari b a b c Universidade Federal do Rio Grande do Sul, UFRGS, Faculdade de Agronomia, Av. Bento Gonçalves, 7712, Porto Alegre, RS 91540-000, Brazil University of Wisconsin — Madison, Department of Soil Science, FD Hole Soils Lab, 1525 Observatory Drive, Madison, WI 53706, USA CAPES Foundation, Ministry of Education of Brazil, Brasília, DF 70040-020, Brazil a r t i c l e i n f o Article history: Received 4 March 2015 Received in revised form 21 July 2015 Accepted 23 July 2015 Available online xxxx Keywords: Soil carbon Subtropical soils Vineyard Carbon stocks Inceptisols Ultisols a b s t r a c t There is a need for soil C assessment in the soils of tropical and subtropical areas. We have aimed to quantify the spatial extent of SOC concentration and stocks under different land use and soil types in an 8118 ha area in southern Brazil. Common soils are Inceptisols, Ultisols and Mollisols, and the dominant land use is forest and vineyard. SOC data were modeled by 5 depths deriving values from spline functions. Regression kriging was used to model SOC concentration for each depth to 100 cm, and for producing a soil depth map. Uncertainty was estimated by empirical approach, using sequential Gaussian geostatistical simulation of the residuals. The Projected Natural Vegetation Soil Carbon (PNVSC) approach was used to evaluate changes in soil carbon due to land use change. Bulk density was estimated by pedotransfer functions. SOC stocks were calculated using the SOC prediction, bulk density and the soil depth map, and the stocks were corrected by cumulative mass coordinates. The models for SOC concentration prediction explained about 44% of the variance at 30–60 cm depth and with slightly lower values for other depths. Important covariates for prediction were Soil Order (Entisols), coordinate X, Aspect and the DEM. The model for the prediction of soil depth explained 43% of variance and important covariates were Soil Order (Entisol, Mollisol, Ultisol), Valley Depth and TWI. Soils under forest accumulated more carbon in the top 30 cm whereas soils under pasture had higher SOC levels with depth. Soils under arable crops and vineyard had the lowest SOC concentration. SOC concentration decreases by depth, as well as prediction intervals of uncertainty, until 60 cm depth. The SOC stocks (0–100 cm) varied between 104 t C/ha in vineyards on Alfisols, and 280 t C/ha in pasture areas on Oxisols. The PNVSC analysis showed that most soils had lost SOC compared to when they were projected to be under forest. Published by Elsevier B.V. 1. Introduction Assessing the amount and distribution of soil organic carbon (SOC) levels is important as it provides information about soil fertility, rates of sequestration of carbon, recovery of degraded soil, or the impact of land use changes. Mapping the SOC concentration and stocks is challenging because of the considerable variation and dynamics. Spatial and temporal SOC changes are affected by natural and anthropic factors including management practices and land use changes. Several recent studies have predicted and mapped SOC (Adhikari et al., 2014; Padarian et al., 2012; Kirsten et al., 2015; Malone et al., 2009; Mendonça-Santos et al., 2010; Ross et al., 2013; Zhang and Shao, 2014) and the estimation is based on relation between covariates (land use, soil type, slope, aspect, etc.) and SOC levels. Different covariates were found in models to explain SOC distribution. Thompson and Kolka (2005) found that more than 71% of SOC variation could be ⁎ Corresponding author. E-mail address: hartemink@wisc.edu (A.E. Hartemink). http://dx.doi.org/10.1016/j.geoderma.2015.07.016 0016-7061/Published by Elsevier B.V. explained by slope, aspect, curvature, topographic wetness index and overland flow distance. Wiesmeier et al. (2014) found that the most important factors to predict SOC stocks were land use, soil type, soil moisture and climate. Adhikari et al. (2014) predicting SOC concentration, at different soil depths, reported that the importance of variables differed by depth. Minasny et al. (2013) synthesized a large number of digital SOC mapping studies and concluded that different covariates could explain the variation of SOC depending on the complexity of the landscape. The majority of SOC inventory assessments to date focused the 0–20 cm or 0–30 cm surface layers, whereas considerable amounts of SOC may be present deeper in the soil profile (Lal, 2005; Rumpel and Kögel-Knabner, 2011; Minasny et al., 2013; Boddey et al., 2010). Sisti et al. (2004) studied SOC stocks down to 100 cm depth with zero tillage and conventional tillage and found, in rotations with vetch planted as a winter green-manure crop, significantly higher soil carbon and nitrogen concentrations under zero tillage, with most of the differences occurring at 30–85 cm depth. Angers and Eriksen-Hamel (2008) showed different interpretation of SOC stocks when considering different depths, in no till and full-inversion tillage. Full-inversion tillage could accumulate more B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 carbon at the bottom of the plow layer, but the SOC does not completely offset the gain under no till in the surface horizon. The authors highlight the importance of taking into account the whole profile to understand the distribution of SOC stocks. Land use has major impacts on SOC concentration and stocks. However, these effects are also affected by soil class and depth (Hartemink and McSweeney, 2014; Nieder and Benbi, 2008). Changes in land use impacts the SOC levels and modifies soil characteristics. Several studies explained the changes of SOC with land use change. Conant et al. (2001), reviewing 115 studies, found that conversion from native land (mostly rain forest) to pasture increased soil C content for nearly 70% of the studies. Guo and Gifford (2002), compiling 74 publications, found that SOC stocks declined after land use changed from pasture to plantation (− 10%), native forest to plantation (− 13%), native forest to crop (−42%), and pasture to crop (−59%). However, the SOC stocks increased when the native forest was converted to pasture (+8%), crop to pasture (+19%), crop to plantation (+18%), and crop to secondary forest (+ 53%). Cerri and Andreux (1990) showed that C levels after 50 years of sugarcane cultivation, in São Paulo, Brazil, were 46% of the levels under primary forest. Although there is a considerable body of research on the digital mapping of SOC in temperate regions, few studies have been conducted in the tropical and subtropical areas. Examples include Berhongaray et al. (2013) estimating SOC stocks in Argentine Pampas, Cheng et al. (2004) predicting SOC concentration in a subtropical area in China, Vasques et al. (2010) estimating SOC stocks in a subtropical watershed in Florida. Digital soil mapping has been used in Brazil (Giasson et al., 2006; Mendonça-Santos and Santos, 2007) and examples of SOC predictions include the studies by Mendonça-Santos et al. (2010) whom used regression-kriging for evaluate the SOC stocks in Rio de Janeiro State, and de Souza et al. (2014) using regression-kriging to predict SOC and clay content in Rio Doce Basin (Minas Gerais State). There have been other studies (e.g., Cerri et al., 2007; Tornquist et al., 2009b) where ecosystem models such as Century or Rothamsed C Model were applied to estimate SOC dynamics in the upper soil layers from different areas in Brazil. The present study aimed to analyze the distribution of soil C in the grape growing region of Vale dos Vinhedos, in Rio Grande do Sul State, Brazil. The objectives were as follows: (i) to quantify and understand the spatial variation of SOC concentration by depth through digital soil mapping, and to assess the uncertainty, (ii) to quantify and map SOC stocks, and (iii) to estimate SOC changes due to land use change. 205 2. Materials and methods 2.1. Study area The study was conducted in the Vale dos Vinhedos (Vineyard Valley) which is a wine production region in northeastern Rio Grande do Sul State (Fig. 1). The study area covered 8118 ha. The climate is classified as Cfb, subtropical with a mild summer, mean annual temperatures of 17.2 °C and 1736 mm annual rainfall (EMBRAPA, 2008). The dominant lithology is effusive rocks mostly from the Mesozoic Era (IBGE, 1986). Lower sequence comprises mostly basalts and diabase dikes, whereas the upper sequence has predominantly acid effusive rocks such as rhyolite and dacites. Average soil depth is 150 cm (range from 25 to N250 cm) and many soils are stony and rocky (average 4.5% of fragments N 20 mm in diameter). In the study area, Inceptisols cover about 44%, Ultisols 29% and Mollisols almost 15% (Fig. 2). Mollisols are mostly present at lower elevations close to valley bottoms in the northern part of the study area. Soils in the western part of the study area are mainly Argissolos (Ultisols and Alfisols), Chernossolos (Mollisols), and Neossolos (Entisols and Mollisols). The eastern part has more rugged terrain and the dominant soils are Neossolos (Entisols) and Cambissolos (Inceptisols), with association of Argissolos (Ultisols and Alfisols), Latossolos (Oxisols) and Nitossolos (Oxisols and Ultisols) (Flores et al., 2012). Forest (44%) and vineyard (31%) are the dominant land use in the study area. Deciduous forest is the main vegetation in plateau rugged areas, and Araucaria forest in flatter areas (IBGE, 1986). 2.2. Soil and environmental data The soil data were obtained from the soil survey project “Os Solos do Vale dos Vinhedos” (Flores et al., 2012). Sample points were selected along predefined paths representing different landscape units (Flores et al., 2012). Sampling was done with 163 total pedons, comprising 580 soil horizons. The soils were analyzed following Brazilian standard methods (Santos et al., 2006): SOC analysis by Walkley–Black wet oxidation. Additionally, in 2014, samples were obtained from 10 pedons (34 horizons) for an estimate of soil bulk density of the Flores et al. (2012) soil survey, allocated by contrasting land uses (vineyard, forest/planted forest, pasture, arable crops, and fallow) and soil classes. The 10 measured bulk density were used to evaluate three pedotransfer functions, which were chosen based on studies that include data from subtropical Fig. 1. Study area (Vale dos Vinhedos) in Rio Grande do Sul, Brazil (8118 ha) and location of the 163 pedons and 10 bulk density pedon sampling points. 206 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 Fig. 2. Land use and soil taxonomy map of Vale dos Vinhedos in Rio Grande do Sul, Brazil. Percentages of different land use and soil order classes in parentheses. soils. Table 1 lists measured bulk density, pedotransfer functions, and validation using root mean square error (RMSE). Based on the lower value of RMSE (0.11), the simplified equation of Benites et al. (2007) — Eq. (2) in Table 1 — was chosen to extrapolate the bulk density for the whole dataset, producing 163 bulk density estimates. This function was developed from a large compilation of pedons from the Brazilian soil survey database maintained by EMBRAPA (Empresa Brasileira de Pesquisa Agropecuária) that include pedons in Rio Grande do Sul State (Tornquist et al., 2009a; Benites et al., 2007). Once the bulk density was calculated, the values were splined to derive bulk density for the 5 GlobalSoilMap standard depths. These values were then attributed to each map unit of Flores et al. (2012) soil map (scale 1:10.000) considering the reference soil profiles, extrapolating then to the whole study area. On SOC concentration and soil depth predictions the following data layers from Flores et al. (2012) were used: 5 × 5 m grid resolution DEM, a soil map (scale 1:10,000) and orthorectified aerial imagery. The DEM was upscaled to 15 m grid cell size. The original soil legend of the Flores et al. (2012) survey, published according to the Brazilian soil classification (SiBCS), was converted to Soil Taxonomy (12th ed, 2014) using pedon data (clay content, pH, thickness, carbon content, texture, color, clay skins and drainage) and additional guidance from the correlation table proposed by Anjos et al. (2012). A land use map was made using the orthorectified mosaic of aerial images from November 2005 (Flores et al., 2012). Initially, a supervised classification was performed after the images were filtered 3 times (3 × 3, 5 × 5, 7 × 7) using the mean. The supervised classification identified land uses for approximately 50% of the area particularly in the forested areas. Land use in the other half area was delimited manually. The final land use map contains 8 classes namely vineyard, forest, planted forest, pasture, arable crops, fallow, building and water bodies. Building and water bodies were masked. A set of terrain attributes was derived from the DEM including Slope, Aspect, Valley Depth, Topographic Wetness Index, Overland Distance to Channel Network and others. A map with 13 landform classes was made in LandMapR software using the DEM (MacMillan, 2003). The covariates used for predicting the SOC levels and soil depth are presented in Table 2. 2.3. Prediction models Following GlobalSoilMap specification (Arrouays et al., 2014) until 1 m depth, equal area splines were used to harmonize the SOC concentration and bulk density data for 5 depth intervals: 0–5, 5–15, 15–30, 30–60, and 60–100 cm. The smoothing parameter lambda chosen was 0.1 (Malone et al., 2009). Table 1 Bulk density (t/m3) for different land use and soil depths (cm), obtained from field measurements (10 soil pits) and pedotransfer functions. Measured values Depth 1 Depth 2 Depth 3 Depth 4 Depth 5 Vineyard Vineyard Vineyard Vineyard Forest Forest Planted Forest Pasture Arable Crops Fallow 1.17 (11 cm) 1.14 (7 cm) 1.13 (9 cm) 1.16 (13 cm) 0.97 (25 cm) 1.02 (20 cm) 1.09 (15 cm) 1.15 (10 cm) 1.10 (7 cm) 1.29 (40 cm) 1.20 (20 cm) 1.17 (16 cm) 1.21 (34 cm) 1.35 (35 cm) 1.07 (44 cm) 1.08 (45 cm) 1.27 (50 cm) 1.16 (33 cm) 1.55 (30 cm) 1.33 (59 cm) 1.22 (35 cm) – 1.22 (60 cm) 1.17 (60 cm) 1.13 (63 cm) 1.28 (75 cm) 1.40 (82 cm) 1.25 (51 cm) 1.44 (45 cm) 1.21 (94 cm) – – 1.25 (81 cm) – 1.23 (85 cm) – 1.33 (124 cm) – 1.28 (73 cm) 1.16 (118 cm) – – – – – – – – – – Pedotransfer functionsa (1) pm ¼ 1:35 þ 0:0045  sand þ 6  10 100 pb ¼ OMð%Þ 100−OMð%Þ Þþð Þ ðp p OM −5 2  ð44:7−sandÞ þ 0:060  log depth Reference RMSE Tranter et al. (2007) 0.16 Benites et al. (2007) Benites et al. (2007) 0.11 0.13 m (2) pb = 1.5688 − 0.0005 ∗ clay − 0.009 ∗ OC 30–30 cm : pb ¼ 1:5544−0:0004  clay−0:01  OC þ 0:0067  SB (3) 30–100 cm : pb ¼ 1:5674−0:0005  clay−0:006  OC þ 0:0076  SB OC (g/kg): organic carbon; SB (cmolc/kg) — sum of basic cations (Ca2+, Mg2+ and K+); clay (g/kg). a pb = bulk density (g/cm3); pm: mineral bulk density (g/cm3); pOM = organic matter bulk density = 0.224 g/cm3; sand (dag/kg); depth (cm). B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 207 Table 2 Variables used in the prediction of SOC content (g/kg) and soil depth of the study area in Vale dos Vinhedos in Rio Grande do Sul, Brazil. Variables Data descriptions Type Mean (min–max) Soil carbon Digital elevation model — 15 m Coordinate X Coordinate Y Slope Aspect Analytical hillshading TWI LS factor Vertical distance to channel network Valley depth Slope height Normalized height Mid slope position Flow direction MRVBF Overland flow distance to channel network Direct insolation Soil order Land use Convexity Topographic position index (TPI) Mass balance index (MBI) Plan curvature Vector ruggedness measure (VRM) LandMapR Elevation above mean sea level UTM latitude UTM longitude Local hill slope gradient Slope aspect Angle between the surface and the incoming light beams Topographic wetness index Slope length factor Altitude above channel network Relative position of the valley Vertical distance from the base of the slope to the crest Height position within a reference area Cover the warmer zones of slopes Direction of the flow Identifies the depositional areas Distance from non-channel cells to channel cells Potential incoming solar radiation Soil order map Land use map Terrain surface convexity Compare elevation of each cell to the neighborhood Balance between soil mass deposited and eroded Curvature in a horizontal plane Measures terrain ruggedness Landform classification Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Numeric Categorical Categorical Numeric Numeric Numeric Numeric Numeric Categorical 541.49 (206.15–723.05) 445052 (438242–451863) 6770978 (6765083–6776873) 13.85 (0–81.01) 180 (0–360) 0.93 (0–2.74) 3.12 (0.27–8.76) 3.71 (0–95.9) 26.86 (0–259.84) 24.48 (0.36–275.18) 24.91 (0.03–309.36) 0.49 (0–1) 0.52 (0–1) 35.06 (1–255) 0.21 (0–4.92) 204.24 (0–1385) 3.29 (0–5.71) 6 classes 6 classes 0.51 (0.26–0.78) −0.05 (−11.14 to 21.97) 0.16 (−0.81 to 1.61) 0 (−0.16 to 0.31) 0.01 (0–0.12) 12 classes X X X X X X X X X X X X X X X X X X X The splined data were randomly split into 75% (122 pedons) for training the model, and 25% (41 pedons) for validation. The training data were used to predict SOC concentrations and all the pedons were used to predict soil depth. Four different regression models were tested: Multiple Linear Regression (MLR), Stepwise Multiple Linear Regression (SMLR), Cubist, and Random Forest. In MLR, each independent variable is weighted by the regression to ensure maximal prediction from the set of independent variables (Hair et al., 2009). The weights denote relative contribution of the independent variables and facilitate to know the influence of each variable. However, correlation among independent variables needs to be considered. In SMLR, each variable is considered to be included prior to developing the equation. The independent variable with the greatest contribution is added first, followed by the variables selected based on their incremental contribution over the variables already in the equation (Hair et al., 2009). The Cubist model is based on the M5 algorithm of Quinlan (1992). The M5 algorithm builds tree-based models, which may have multivariate linear models at their leaves (Quinlan, 1992). It first partitions the data into subsets within which their characteristics are similar with respect to the target variable and the covariates. There are several rules arranged in hierarchy. The Random Forest is an ensemble learning method for classification (and regression) that operate by constructing a multitude of decision trees at training time which are later aggregated to give one single prediction for each observation in a dataset. For regression, the prediction is the average of the individual tree outputs (Breiman, 2001; Malone, 2013). Based on similarity of results with the original values (Fig. 3), MLR proved to be the most robust model to predict SOC concentration and it was chosen to model SOC concentration and soil depth. Then, two sets of MLR models were implemented, one set for the SOC concentration (5 models, one for each depth) and one for the soil depth. Residual values (the difference between predicted and observed) were calculated for each model, and spatial relation was modeled with variograms. Kriging of the residuals was performed for the entire area, and the results were added to MLR estimation. The relative importance of the variables for each model was estimated based on absolute value of t-statistics. The final results for SOC concentration maps were refined replacing negative values by zero. The soil depth map had values ranges between 0 and 250 cm. The map was sliced into 5 layers: 0–5 cm, 5–15 cm, 15–30 cm, 30–60 cm, Soil depth X X X X X X X X X X X X X X X X X X X 60–100 cm, creating 5 sets of thickness data. The thickness data were used to calculate SOC stocks, by each depth intervals. The gravel and stone contents were obtained from the 163 pedons (Flores et al., 2012) and the distribution by depth was estimated by equal area splines. The values were extrapolated to the entire area through reference profiles of soil map units (Flores et al., 2012). To calculate SOC stocks in t/ha, SOC concentrations in mass fraction were multiplied by bulk density previously calculated and mapped (Section 2.2) and thickness for each depth, and corrected for gravel and stone contents, according to the following equation: SOC  


 h g i ton g  thickness ½ cm Š =10 ¼ SOC  BD 3 ha kg  cm gravels ½%Š  1− : 100 ð1Þ To compare SOC stocks in soils under different land use and soil types, the results needed to be corrected by mass, avoiding carbon stock variation due to bulk density changes. The cumulative mass approach should be preferred as the basis for carbon stock accounting on a fixed mass per unit area (Minasny et al., 2013). The approach from Gifford and Roderick (2003) was used to calculate the cumulative mass and SOC stocks down to 1 m profile. This approach corrects SOC stocks using a reference cumulative mass. Soil mass of the forest areas were chosen as reference, as represent mass of soils under natural vegetation, and were calculated by the measured bulk density splined and the respective thickness. The reference mass by interval depth were 4.95 g/cm2 for 0–5 cm, 9.9 g/cm2 for 5–15 cm, 15.15 g/cm2 for 15– 30 cm, 33.6 g/cm2 for 30–60 cm and 47.6 g/cm2 for 60–100 cm. For the whole area, the soil mass for each depth was calculated by the bulk density maps and the thickness layers derived from the soil depth map. Then, the reference soil mass, the soil mass for each depth of the entire study area, and the previously calculated SOC stocks were each one cumulatively summed. The cumulative corrected SOC stocks to the entire area, for each depth, were calculated through the equation applied to each pixel as follows: cs ðt Þ ¼ cs ðza Þ þ cs ðzb Þ−cs ðza Þ ðms ðt Þ−ms ðza ÞÞ ms ðzb Þ−ms ðza Þ ð2Þ 208 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 Fig. 3. a) Example of distribution of predicted × observed values, depth 30 to 60 cm, and b) validation of SOC concentration prediction for all depth intervals, by 4 different methods. B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 209 Fig. 4. Histograms and variograms of residuals (observed–predicted), from SOC concentration and depth predictions. where cs(t) is the value of cumulative SOC stocks corrected by mass; cs(za) and ms(za) are the value of cumulative SOC stocks and mass, respectively, from the lower boundary of the layer above it; cs(zb) and ms(zb) are the cumulative SOC stocks and mass of the lower boundary of the current layer; ms(t) is the cumulative soil mass from the lower depth of the reference layer. The SOC stocks for each interval depth was calculated by subtracting the cumulative SOC stocks of the lower and upper limit from respective layer. values. RMSE correspond to root mean square error, ME to the mean error, and CCC to the Lin's Concordance Correlation Coefficient. The R2 was obtained directly from the model in R, whereas other parameters were calculated as follows: ME ¼ 1 Xn ^zðxi Þ−zðxi Þ 1¼1 n RMSE ¼ 2.4. Prediction evaluation CCC ¼ The SOC concentration models were validated with 25% of the data, and the soil depth model with the whole dataset, using 4 statistical parameters: RMSE, ME, R2 and CCC. The R2 is the coefficient of determination of linear regression, between the observed values and predicted ð3Þ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 Xn 2 ½zðxi Þ−^zðxi ފ i¼1 n 2  ρ  σ ^zðxi Þ  σ σ ^2zðx Þ i ð4Þ zðxi Þ 2 þ σ 2zðxi Þ þ ð^zðxi Þ−zðxi ÞÞ ð5Þ where n is the number of the validation sample points, z(xi) is the observed value, ẑ(xi) is the predicted value, σ 2zðxi Þ and σ ^2zðxi Þ are the 210 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 Table 3 Descriptive statistics of training, validation, and estimated SOC content and soil depth. SOC content Training data n = 122 points Validation data n = 44 points Estimates n = 312,790 pixels 0–5 cm Mean Median Min Max 27.5 23.8 4.6 93.5 24.7 22.7 7.0 61.0 31.5 31.1 0 103.8 5–15 cm Mean Median Min Max 27.5 23.5 4.7 95.3 24.8 23.0 7.0 61.6 31.6 31.2 0 108.6 15–30 cm Mean Median Min Max 23.3 19.9 4.6 90.3 21.9 20.7 7.0 59.6 26.5 25.9 0 176 30–60 cm Mean Median Min Max 12.2 10.1 0 59.5 10.7 9.4 0 40.9 13.1 12.5 0 60.1 60–100 cm Mean Median Min Max 7.7 6.1 0 59.5 6.4 5.9 0 26.2 9.1 8.6 0 59.5 Soil depth Mean Median Min Max n = 163 points 149.4 150 25 250 n = 163 points 149.4 150 25 250 2.6. SOC changes n = 312,790 pixels 148.7 150 0 250 variances, and ρ is the correlation coefficient between the predictions and observations. The impact of each variable was measured by the absolute value of t-statistics for each model parameter obtained through MLR. 2.5. Uncertainty and probability maps Estimating uncertainty is complex considering all the sources of uncertainty. There are a number of approaches to estimate the uncertainty and Malone et al. (2011) and Shrestha and Solomatine (2006) suggest the empirical approach. In this approach, the residuals between modeled outputs and corresponding observed data are used to formulate prediction intervals (PIs). The uncertainty is expressed in the form of two quantiles of the underlying distribution of model error (residuals). The PI takes into account all sources of uncertainty and circumvents attempts to separate out the contribution of each source of uncertainty (Malone et al., 2011; Shrestha and Solomatine, 2006; Solomatine and Shrestha, 2009). The methodology is independent of the prediction model structure, as it requires only the model outputs. Table 4 Validation of the Multiple Linear Regression and regression kriging for predicting SOC content (g/kg) and soil depth (cm). Soil depth 0–5 5–15 15–30 30–60 60–100 Depthb Multiple Linear Regression 2a R RMSE 0.33 0.33 0.34 0.44 0.34 0.43 13.23 13.36 12.37 6.62 4.77 34.78 a Regression kriging a CCC R2a RMSEa MEa CCCa 4.89 4.80 3.76 3.04 2.26 0 0.38 0.38 0.43 0.49 0.41 0.59 0.34 0.33 0.35 0.48 0.41 – 12.82 13.00 12.00 5.80 4.44 – 4.09 3.97 3.10 2.44 1.87 – 0.39 0.39 0.45 0.58 0.52 – ME a We used the empirical approach estimating PIs through the residuals of SOC predictions. Between several methods for modeling the distribution of residuals, we chose sequential Gaussian geostatistical simulations because it is more related to the spatial method used for SOC prediction. Firstly, the residuals from MLR prediction of SOC, at each 5 standard depth, were simulated with 100 iterations and then the outputs were added back to the predicted SOC concentration. For each predicting pixel, we considered the two percentiles, lower 5% and upper 95%, covering the 90% PI, as suggested in GlobalSoilMap specifications (Arrouays et al., 2014). Lower and upper limits were mapped (Fig. 5) and the uncertainty models were evaluated on the 25% validation dataset (Fig. 9). With the 100 values of SOC concentration, we applied Eq. (1) for produced SOC stocks and Eq. (2) to correct by cumulative mass. The results were used to produce maps of probability of total SOC stock (0–100 cm) that exceed a threshold of 184 t C/ha. The value of 184 t C/ha is based on the averaged SOC stocks under forest for the entire study area. Areas with high probability of exceeding this limit are likely to have the same SOC stocks as under forest. The number of times that pixels values exceeded the threshold, between 100, was counting and recording for producing the maps. The following probabilities were considered for mapping: 20%, 40%, 60% and 80%. a R2 = coefficient of determination, RMSE = root mean square error, ME = mean error, CCC = Lin's Concordance Correlation Coefficient. b Depth model used the whole data samples, and the validation was made based on training data. SOC changes due to land use changes were estimated using Projected Natural Vegetation Soil Carbon (PNVSC) approach (Waring et al., 2014). PNVSC is considered a projected SOC that could be present today if the area was under natural vegetation. The PNVSC maps were elaborated re-applying the equations produced by MLR models for SOC concentration (Section 2.3), nevertheless with the coefficients for land use types other than forest set to zero. The produced maps are hypothetically representing soil carbon which could be observed today if the whole study area remained under natural vegetation. The predicted SOC concentration can now to be compared with PNVSC by Eq. (6) to estimate SOC changes due to land use change (e.g. Adhikari and Hartemink, 2015): SOC changes ¼ SOC predicted –PNVSC: ð6Þ Negative SOC change indicates that the soil has less SOC compared to the projected natural vegetation (forest) whereas positive SOC change indicate that the soils have accumulated SOC. 3. Results 3.1. SOC prediction and model comparison While comparing four prediction methods using the training data, Cubist and Random Forest showed a high R2 (N0.92) and CCC (N0.8) for SOC prediction at all depths, compared to MLR and SMLR with lower values (R2 b 0.51 and CCC b 0.64). Similarly, both Cubist and Random Forest had lower RMSE (b6.4 g/kg) than MLR and SMLR (RMSE N 6.7), when comparing all the soil depths. However, when using the validation samples (25% of pedons), MLR had a higher R2 and CCC and a lower RMSE than the other models (Fig. 3b). Comparing the distribution of observed and predicted values (Fig. 3a), MLR had less spread of points. The MLR model suffered from the higher bias (ME) compared to all other methods. RMSE did not differ much between methods with Cubist showing the highest RMSE at all depths. Based on R2 and CCC values, and considering the RMSE not so different between methods, MLR was the best model to estimate the SOC concentration. The high bias indicates that MLR might overestimate the predicted values and, therefore, it should be considered when interpreting the results. Based on these findings, we assumed that B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 MLR could be the appropriate method for SOC concentration and soil depth prediction. After the predictions were made by the MLR models, the distribution of prediction residuals and their spatial dependence was analyzed and plotted (Fig. 4). Spatially, the residuals were poorly auto-correlated for the top three depths (0–5, 5–15, and 15–30 cm), whereas a better spatial structure was observed below 30 cm soil depth. Residuals of soil depth prediction were normally distributed with no spatial autocorrelation as suggested by the pure nugget effect of the variogram. 3.2. Evaluation of MLR model for SOC and soil depth prediction Descriptive statistics of training data, validation data, and the estimates are shown in Table 3. The mean SOC concentration for the validation are slightly lower than for training data. The estimated data have higher mean, median and maximum values than the training data which suggests that the MLR model can overestimate SOC concentration. The bias of MLR is depicted in Fig. 3b and in Table 4, showing higher values at 0–5 cm soil depth and decreasing until depth 60–100 cm. For the soil depth, the mean of estimated data were similar to training data. Validation results of the MLR model is shown in Table 4. The R2 between predicted and measured values differed by depth and was highest at 30–60 cm, with value of 0.44, and CCC of 0.49. For all other depths, R2 was between 0.33 and 0.34, and values of CCC were between 0.38 and 0.43. The RMSE and ME decreased with increasing soil depth. When the residuals were added to the MLR predictions, the R2 and CCC increased and RMSE and ME decreased (Table 4). For the soil depth prediction model, CCC of 0.59, R2 of 0.43, and RMSE of about 34.8 cm were observed. The high values of R2 and CCC were probably due to the use of same samples for model training and validation. 211 3.3. Spatial predictions and variable importance In general, SOC levels differed by depth, soil order and by land use type. SOC concentration decreased below 15 cm depth (Table 5 and Fig. 5). The mean values (Table 5) vary between 5.8 g C/kg, from vineyard areas in Alfisols at 60–100 cm depth, and 43.9 g C/kg, from pasture areas in Entisols at 15–30 cm depth. Entisols have the highest mean SOC concentration, 39.1 g C/kg at 5–15 cm depth and Alfisols the lowest, 7.1 g C/kg at depth 60–100 cm (Table 7). Similarly, forest has the highest mean SOC concentration, 36.1 g C/kg at 5–15 cm depth, and arable crops the lowest, 6.7 g C/kg, at depth 60–100 cm. The importance of the variables for SOC concentration prediction differed by depth. The relative importance of the 15 main variables in SOC concentration and the soil depth model is presented in Fig. 6. Up to 30 cm soil depth, the most important variable was Soil Order (Entisols), coordinate X, Aspect and DEM. Below that soil depth the important variables were as follows: Overland Flow Distance to Channel Network, Aspect, Soil Order (Entisols and Oxisols), coordinate Y, and Normalized Height. Overall, the Entisols soil order was a good predictor. Descriptive statistics of soil depth data and its prediction are shown in Table 3, and the predicted map in Fig. 7. Soils shallower than 70 cm occupied 1% of area (81 ha) and most of them were Entisols (65%) and Mollisols (33%). Soils deeper than 200 cm occupied 5% of area (439 ha) and most of them were Ultisols (54%) and Mollisols (20%). Soils between 70 and 200 cm occupied the largest area (94%) and most of them were Inceptisols (43%), Ultisols (28%), and Mollisols (16%). The deepest soils were Ultisols (169 cm), followed by Oxisols (158 cm), Inceptisols (150 cm), Alfisols (142 cm), Mollisols (134 cm) and Entisols (110 cm). Soil depth increased in the northern part of the study area and it varied mainly with slope as shallower soils were found on steeper slopes. Table 5 Predicted SOC content (g/kg) by soil order and land use types, from the study area in Vale dos Vinhedos in Rio Grande do Sul, Brazil. Soil order Land use 0–5 cm 5–15 cm 15–30 cm 30–60 cm 60–100 cm Alfisol Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard 26.1 (±1.4) 27.2 (±5.1) 28.1 (±5.4) 18.8 (±6.2) – 20.5 (±5.3) 41.3 (±0.7) 37.9 (±8.7) 43.1 (±8.7) 39.5 (±8.2) 30.8 (±5.3) 31.5 (±6.9) 29.2 (±4.9) 33.6 (±6.3) 37.0 (±7.0) 33.2 (±6.4) 24.9 (±4.1) 27.4 (±7.0) 27.5 (±9.3) 33.7 (±7.4) 37.0 (±8.5) 32.4 (±11.3) 19.7 (±3.2) 29.4 (±8.9) 32.1 (±4.8) 38.6 (±3.3) 40.2 (±6.9) 34.2 (±4.6) – 33.5 (±4.7) 21.6 (±6.7) 27.7 (±5.8) 30.8 (±7.1) 25.5 (±6.9) 17.5 (±3.7) 21.6 (±6.9) 26.0 (±1.4) 26.7 (±5.2) 27.9 (±5.5) 19.0 (±6.1) – 20.2 (±5.4) 41.7 (±0.7) 38.0 (±8.9) 43.7 (±8.9) 40.4 (±8.3) 31.2 (±5.4) 31.7 (±7.1) 29.3 (±5.0) 33.2 (±6.3) 37.0 (±7.1) 33.7 (±6.4) 25.0 (±4.2) 27.3 (±7.1) 27.5 (±9.4) 33.4 (±7.7) 37.3 (±8.7) 32.6 (±11.5) 19.9 (±3.2) 29.3 (±9.1) 32.2 (±5.0) 38.3 (±3.5) 40.1 (±6.9) 34.4 (±4.7) – 33.5 (±4.7) 21.8 (±6.7) 27.5 (±5.9) 31.0 (±7.3) 26.1 (±7.0) 17.7 (±3.7) 21.7 (±7.1) 19.3 (±2.2) 17.5 (±5.8) 18.8 (±5.7) 18.3 (±5.7) – 13.7 (±5.5) 36.1 (±0.7) 33.1 (±9.1) 40.9 (±10.4) 43.9 (±8.2) 31.1 (±5.6) 29.1 (±7.8) 24.8 (±5.5) 25.1 (±6.4) 29.7 (±7.0) 34.2 (±6.3) 23.4 (±4.2) 21.9 (±6.9) 22.0 (±8.4) 25.2 (±8.8) 31.4 (±9.0) 31.4 (±10) 19.8 (±4.1) 23.5 (±9.3) 33.4 (±5.5) 34.9 (±4.7) 37.1 (±6.1) 39.9 (±4.9) – 33.7 (±4.4) 19.6 (±6.1) 22.4 (±6.4) 26.3 (±7.8) 29.0 (±6.6) 19.5 (±3.6) 19.3 (±7.4) 10.2 (±2.4) 10.5 (±5.2) 8.7 (±4.8) 12.0 (±5.0) – 7.9 (±4.5) 16.2 (±1.2) 17.3 (±5.0) 16.9 (±6.4) 24.7 (±4.5) 16.8 (±6.9) 13.8 (±5.3) 13.4 (±4.9) 13.8 (±5.7) 14.2 (±6.1) 21.8 (±5.3) 17.6 (±4.2) 12.2 (±5.6) 10.6 (±4.5) 12.9 (±5.0) 11.1 (±5.3) 17.3 (±3.0) 12.6 (±3.3) 11.7 (±5.4) 28.8 (±3.6) 29.8 (±3.0) 28.5 (±4.7) 34.6 (±3.7) – 29.9 (±3.3) 11.9 (±5.1) 13.5 (±4.4) 12.5 (±5.2) 19.5 (±3.7) 16.1 (±3.2) 11.3 (±4.7) 7.8 (±1.6) 7.9 (±4.2) 8.5 (±4.2) 9.2 (±4.6) – 5.8 (±3.8) 13.0 (±1.0) 11.0 (±4.3) 11.9 (±5.4) 15.4 (±3.7) 9.2 (±5.5) 7.9 (±4.2) 7.8 (±3.8) 8.9 (±5.8) 11.8 (±6.0) 15.3 (±4.6) 12.0 (±4.3) 7.8 (±4.9) 5.7 (±3.5) 6.8 (±4.0) 7.5 (±3.7) 9.8 (±2.4) 7.3 (±2.5) 6.4 (±3.8) 9.1 (±2.8) 13.5 (±2.2) 12.2 (±3.6) 13.4 (±3.3) – 11.8 (±2.7) 5.6 (±3.4) 8.6 (±3.8) 9.8 (±4.6) 12.5 (±3.0) 9.9 (±2.6) 6.8 (±3.9) Entisol Inceptisol Mollisol Oxisol Ultisol 212 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 Fig. 5. Prediction of SOC content (g/kg) and lower (5%) and upper limit (95%) for five soil depths of Vale dos Vinhedos in Rio Grande do Sul, Brazil. Pedotransfer function estimated bulk density for all the pedons, with average of 1.17 g/cm3 (0–5 cm), 1.18 g/cm3 (5–15 cm), 1.19 g/cm3 (15–30 cm), 1.26 g/cm3 (30–60 cm) and 1.27 g/cm3 (60–100 cm). The values ranged between 0.54–1.4 g/cm3 (0–5 cm), 0.56–1.4 g/cm3 (5–15 cm), 1.19–1.4 g/cm3 (15–30 cm), 1.26–1.47 g/cm3 (30–60 cm) and 1.27–1.47 g/cm3 (60–100 cm). Fig. 8 shows SOC stock maps for each 5 depth, and the total stock for 0–100 cm. Overall, it appeared that the spatial distribution of SOC stocks was similar to SOC concentration. Values were higher on the valley banks and bottom valley, which were under forest and with reduced agricultural use. Total SOC stocks were highest in Oxisols (230–280 t C/ha) and lower in Alfisols (104–143 t C/ha), as in Table 6. Soils under pasture B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 213 Fig. 6. Relative importance of the 15 variables used for predicting SOC content at each soil depth. The importance is calculated based on the absolute value of the t-statistics for each model parameter (see Table 1 for a description of the variables). areas had the highest SOC stocks (139–280 t C/ha) and soils under planted forest areas the lowest SOC stocks (116–174 t C/ha). Oxisols under pasture areas had the highest SOC stocks (280 t C/ha) and Alfisols under vineyard the lowest (104 t C/ha). 3.4. Uncertainty and probability maps For uncertainty of SOC concentrations prediction, calculated by empirical approach and mapped (Fig. 5), the averages for the lower limit of Fig. 7. Soil depth of the study area in Vale dos Vinhedos in Rio Grande do Sul, Brazil. 214 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 Fig. 8. Estimation of SOC stocks (t C/ha) of the study area in Vale dos Vinhedos in Rio Grande do Sul, Brazil. prediction decreased from 10.5 g C/kg at 0–5 cm soil depth to 1.5 g C/kg at 60–100 cm depth. The means for upper prediction limit decreased from 53.8 g C/kg at 0–5 cm soil depth to 19.4 g C/kg at 60–100 cm soil depth. A similar trend was found for the difference in the lower and upper limits. The uncertainty values of nine sample points, from the validation dataset (25% of pedons), are shown in Fig. 9. The blue line represents estimated value, and red lines represent the low (left) and the upper limit (right) for the 5 depths. Bars represent the splined SOC values, harmonized by depth of GlobalSoilMap. The prediction intervals are higher B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 215 Table 6 Calculated SOC stocks (t C/ha) by soil order and land use types for the study area in Vale dos Vinhedos in Rio Grande do Sul, Brazil. Soil order Land use 0–5 cm 5–15 cm 15–30 cm 30–60 cm 60–100 cm Total 0–100 cm Alfisol Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard Arable crops Fallow Forest Pasture Planted forest Vineyard 13 (±1) 12 (±2) 11 (±3) 8 (±3) – 9 (±2) 17 (±1) 14 (±4) 16 (±4) 14 (±4) 12 (±3) 12 (±3) 13 (±3) 14 (±3) 15 (±4) 14 (±4) 11 (±3) 11 (±3) 11 (±3) 12 (±3) 11 (±4) 11 (±3) 7 (±2) 11 (±4) 16 (±2) 19 (±2) 20 (±3) 17 (±3) – 17 (±2) 10 (±3) 13 (±3) 14 (±3) 12 (±3) 8 (±2) 10 (±3) 25 (±2) 23 (±4) 23 (±5) 16 (±6) – 17 (±5) 34 (±3) 28 (±8) 33 (±8) 28 (±8) 24 (±6) 23 (±6) 26 (±6) 29 (±7) 31 (±8) 29 (±8) 22 (±5) 23 (±7) 22 (±6) 24 (±6) 22 (±9) 23 (±6) 14 (±5) 21 (±8) 32 (±5) 38 (±3) 40 (±7) 33 (±5) – 33 (±5) 21 (±6) 26 (±6) 28 (±7) 24 (±6) 17 (±4) 20 (±6) 30 (±3) 26 (±7) 27 (±7) 25 (±9) – 20 (±7) 45 (±4) 40 (±10) 51 (±15) 49 (±12) 37 (±9) 35 (±9) 35 (±9) 35 (±9) 40 (±10) 46 (±10) 32 (±8) 30 (±9) 27 (±9) 29 (±9) 30 (±11) 34 (±8) 21 (±7) 27 (±12) 50 (±8) 53 (±7) 56 (±9) 59 (±9) – 51 (±7) 29 (±8) 34 (±9) 38 (±10) 41 (±9) 28 (±6) 28 (±10) 40 (±7) 39 (±17) 36 (±14) 45 (±15) – 30 (±14) 46 (±10) 51 (±16) 58 (±28) 71 (±28) 47 (±30) 42 (±22) 47 (±15) 48 (±18) 51 (±19) 73 (±18) 55 (±16) 42 (±17) 29 (±12) 42 (±18) 45 (±17) 51 (±12) 42 (±10) 38 (±18) 95 (±12) 100 (±10) 95 (±15) 113 (±14) – 100 (±11) 43 (±16) 50 (±14) 49 (±16) 70 (±13) 56 (±10) 42 (±16) 34 (±9) 38 (±19) 39 (±19) 45 (±19) – 29 (±18) 54 (±10) 37 (±18) 36 (±20) 50 (±23) 28 (±22) 28 (±18) 40 (±18) 43 (±27) 52 (±26) 72 (±22) 54 (±18) 38 (±21) 22 (±13) 30 (±19) 36 (±17) 36 (±18) 33 (±11) 27 (±16) 37 (±14) 59 (±10) 53 (±18) 58 (±15) – 51 (±13) 31 (±16) 44 (±18) 47 (±21) 64 (±14) 53 (±13) 36 (±19) 143 (±18) 137 (±46) 135 (±43) 139 (±50) – 104 (±40) 197 (±15) 170 (±39) 194 (±57) 212 (±54) 147 (±60) 140 (±44) 160 (±44) 170 (±55) 189 (±56) 235 (±55) 174 (±43) 144 (±49) 111 (±38) 137 (±44) 144 (±43) 155 (±36) 116 (±27) 124 (±49) 230 (±38) 268 (±30) 263 (±49) 280 (±40) – 251 (±33) 135 (±44) 167 (±44) 176 (±50) 212 (±39) 162 (±29) 136 (±47) Entisol Inceptisol Mollisol Oxisol Ultisol in upper layers than in lower layers. Of the 41 validation samples the following number were within prediction intervals: 36 for 0–5 cm depth, 34 for 5–15 cm depth, 34 for 15–30 cm depth, 38 for 30–60 cm depth, and 39 for 60–100 cm soil depth. More than 90% of the validation samples were within the prediction intervals derived from residuals with higher spatial covariance (30–60 cm and 60–100 cm). For SOC stocks, the probability maps (Fig. 10) show areas where the SOC stock exceeds the threshold value at 20, 40, 60 and 80% probabilities. The probability for SOC stocks exceeding the limit is highest in the valley bottoms and in the eastern part of study area. There is an 80% probability of SOC stocks to exceed 184 t C/ha in about 13% (1029 ha) of the area. 3.5. SOC changes The mean values of SOC predictions and PNVSC values are given in Table 7 where the data were aggregated by soil order and land use. Areas where SOC has been lost as compared to the same soils under forest are given in bold. SOC has been lost at 0–5 and 5–15 cm soil depth for all soil orders and land use types (except forest which was used as a reference). This loss is also observed at 15–30 cm and 60–100 cm depth, except for Oxisols and pasture. At 30–60 cm soil depth SOC levels has been increased in all soil orders and land use types. The maps of PNVSC and SOC changes are given in Fig. 11. 4. Discussion This study predicted SOC concentration and SOC stocks in a subtropical area under different land use and a range of soil orders. The impact of land use on soil C was evaluated by comparing the SOC concentration under current use with a projected SOC that could be present today if the area was under natural vegetation. In this discussion, we shall focus on the methods of prediction, the effect of the variables used for prediction, and the distribution of SOC under different land uses and soil types. 4.1. Prediction model The different methods tested for regression showed that model evaluation it's more reliable when using a separate validation dataset. Predicted values might be very similar to observed values, when considering the training model. This model may overfit the data and the performance can be poor using validation data. Minasny and McBratney (2013), observing the behavior of a random forest model, concluded that it can easily overfit the data. In our study, the Cubist and Random Forest models seem to overfit the data, whereas MLR produced estimation closer to validation data. SOC concentrations were predicted based on regression kriging Model (MLR and kriging of residuals). The prediction showed the variation in SOC concentration spatially and by depth, land use and soil order. The model explained only part of the variation and when comparing the estimated mean, median and maximum values, our estimation from the model produced slightly higher SOC concentration than training data. This can be explained by the biased estimate when using a nonprobability sample to calibrate the model or also some regions of the feature space to be over or under-represented in the training data. The values of validation parameters such as R2 and CCC were higher for 30–60 cm soil depth and were lower at other depth intervals. The 216 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 Fig. 9. Examples of uncertainty prediction intervals, for SOC levels, of 9 independent validation points. Predicted SOC values are shown in blue, and the lower (5%) and upper limit (95%) in red. Bars represent the SOC values of validation points obtained from spline functions, and harmonized by GlobalSoilMap depths. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) validation results, in Table 4, are comparable to most recent studies predicting SOC. For example, on temperate areas, Adhikari et al. (2014) found the model could explain 43% of variation in validation data, whereas Malone et al. (2009) found R2 values of validation points ranging between 20% and 27%. Other studies present similar results (Brogniez et al., 2014; Collard et al., 2014; Forges et al., 2014; Wiesmeier et al., 2014). The soil depth model could explain 43% of the variation, using all data for estimation and validation. The soil depth map followed the topographic variation, showing the deeper soils in valley bottom. The calculated bulk density varied between 0.54 and 1.47 g/cm3 and were similar to the values found by Tornquist et al. (2009a), between 0.4 and 1.4 g/cm3. 4.2. Importance of predictor variables The relative importance of each variable was evaluated by absolute t-values. The t-value is model dependent, which means that if two or more variables are correlated with SOC concentration, and also correlated with each other, then only one variable may appear with the high tvalue. We noted that variable importance differed by soil depth. Up to 30 cm soil depth, the covariates Soil Order, coordinate X, Aspect and DEM were good predictors. Soil Order (Entisols) contributed mainly due its consistent higher SOC values (Table 5). There was a decrease in SOC concentration towards the west (Fig. 5) and hence coordinate X was important to identify this variation in east–west direction. There was a higher SOC concentration in the soils of the north in the valley bottom, and coordinate Y identifies this variation. In correlation analysis, it was noted that Y has a correlation of − 0.47 with X, which is fairly high compared to other covariates. Both coordinates could explain the spatial variation of SOC concentration, although only X showed high t-value, and to separate individual effect in prediction is not straightforward (Hair et al., 2009). The north-facing slopes receive more solar radiation, and as a result possibly enhanced SOC decomposition and lower SOC levels. This effect can be seen at slightly higher SOC values in the northeast (slope south-facing) compared to the southwest (slope north-facing). This variation could be identified by the Aspect covariate. At lower elevation, temperatures increases and likely the soils contain less carbon due to higher rates of decomposition. However, the elevation was a proxy for deposited material and areas at lower elevation had deeper soils with more SOC. There was a relatively high and negative correlation (−0.55) between DEM and Valley Depth. Only DEM is showed with high t-value, but both explain the SOC variation related with elevation. For the layers below 30 cm soil depth the covariates Overland Flow Distance, Aspect, Soil Order, coordinate Y, and Normalized Height were important predictors for SOC concentration. Overland flow distance to channel network indicate that the SOC concentration is higher closer to channel network, possibly because of organic material deposits under dense vegetation. Libohova et al. (2014) found that areas with water accumulation for longer time periods stored 50–68% more total SOC compared to drier areas. Noticeable influence of soil orders covariates (Entisol, Oxisol or Inceptisol) in SOC prediction was found up to 60 cm depth but not below this depth. The coordinate Y is consistent with the valley bottom in north direction. The Normalized Height indicates the height relatively to the highest and lowest position within an area (Dietrich and Böhner, 2008) and this covariate correlates with Overland Flow Distance to Channel Network (0.63). B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 217 Fig. 10. Maps of different probabilities that the soil contain at least 184 ton SOC/ha in Vale dos Vinhedos in Rio Grande do Sul, Brazil. For prediction of soil depth, Soil Order (Entisol, Mollisol and Ultisol) and Valley Depth proved good predictors. The Entisols are shallower soils (mean depth 110 cm) and Mollisols and Ultisols are the deeper soils. Although Oxisols are also deep soils, it had no significant impact on the soil depth model possibly because of the limited number of samples. 4.3. SOC concentration and stocks The SOC concentration predicted for soils under forest and pasture differed by depth. In the upper layers, soils under forest had higher values whereas soils under pasture had more SOC with depth (Tables 5 and 7). Forest has larger amounts of litter and Table 7 Predicted SOC content and Projected Natural Vegetation Soil Carbon (PNVSC), by soil order and land use. Figures in bold indicate that SOC was lost based on the PNVSC approach (SOC content predicted — PNVSC). SOC and PNVSC (g/kg) — mean values (±standard deviation) Soil order 0–5 cm PNVSC 5–15 cm PNVSC 15–30 cm PNVSC 30–60 cm PNVSC 60–100 cm PNVSC Alfisol Entisol Inceptisol Mollisol Oxisol Ultisol 24.2 (±6.5) 38.7 (±9.7) 32.3 (±8.3) 35.0 (±9.2) 35.1 (±6.1) 26.4 (±8.1) 27.0 (±5.0) 42.1 (±6.6) 35.9 (±6.4) 36.6 (±6.0) 38.2 (±3.1) 29.7 (±5.8) 23.9 (±6.6) 39.1 (±10.0) 32.2 (±8.4) 35.2 (±9.4) 35.1 (±6.1) 26.5 (±8.2) 26.8 (±5.0) 42.6 (±6.7) 35.9 (±6.5) 36.8 (±6.1) 38.1 (±3.1) 29.9 (±5.8) 16.2 (±6.1) 36.4 (±11) 26.0 (±7.9) 29.3 (±9.7) 35.7 (±5.7) 23.0 (±8.1) 17.6 (±3.8) 38.5 (±5.9) 28.0 (±5.2) 29.9 (±5.3) 35.5 (±4.0) 24.8 (±4.9) 8.4 (±4.7) 15.9 (±6.2) 13.5 (±6.0) 11.4 (±5.3) 30.3 (±4.4) 12.4 (±5.1) 7.2 (±2.8) 15.5 (±4.8) 12.6 (±4.7) 11.0 (±3.5) 26.9 (±3.0) 11.3 (±3.5) 7.1 (±4.2) 10.5 (±5.3) 9.9 (±5.8) 7.3 (±3.8) 11.8 (±3.3) 8.5 (±4.4) 7.3 (±2.7) 10.8 (±4.0) 10.3 (±4.6) 7.8 (±2.6) 11.7 (±1.8) 8.9 (±3.0) Land use Arable Crops Fallow Forest Pasture Planted Forest Vineyard 25.4 (±7.8) 30.9 (±7.2) 35.9 (±6.5) 30.1 (±8.5) 23.8 (±6.0) 26.0 (±7.9) 29.5 (±4.3) 32.2 (±3.9) 35.9 (±6.5) 32.8 (±4.2) 36.6 (±2.5) 33.9 (±4.8) 25.5 (±7.9) 30.7 (±7.3) 36.1 (±7.0) 30.5 (±8.6) 23.9 (±6.1) 26.0 (±8.0) 29.5 (±4.3) 32.3 (±3.9) 36.1 (±7.0) 32.8 (±4.2) 36.6 (±2.5) 33.9 (±4.9) 23.3 (±8.1) 24.2 (±7.4) 30.2 (±7.2) 32.3 (±8.1) 23.5 (±5.6) 21.8 (±8.0) 24.4 (±3.7) 25.9 (±3.5) 30.2 (±7.2) 26.3 (±3.8) 29.5 (±2.4) 26.6 (±4.5) 15.2 (±8.1) 13.7 (±5.1) 13.1 (±5.2) 21.1 (±5.8) 16.9 (±4.6) 12.0 (±5.5) 13.9 (±3.1) 11.8 (±3.1) 13.1 (±5.2) 12.7 (±2.8) 14.2 (±2.6) 11.4 (±3.9) 6.7 (±3.7) 8.6 (±4.7) 10.1 (±4.7) 13.3 (±4.1) 10.8 (±4.3) 7.4 (±4.4) 9.1 (±2.0) 9.3 (±3.0) 10.1 (±4.7) 9.5 (±2.1) 11.7 (±2.6) 8.9 (±3.3) 218 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 Fig. 11. Maps of Projected Natural Vegetation Soil Carbon (PNVSC) and changes in SOC in Vale dos Vinhedos in Rio Grande do Sul, Brazil. organic material, which is incorporated into the soil. Aboveground input and relatively low rates of decomposition generally increases topsoil SOC levels compared to grasslands (Don et al., 2011; Guo and Gifford, 2002; Jobbágy and Jackson, 2000). For pasture, deep roots contribute to the accumulation of SOC with depth (Guo and Gifford, 2002). B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 219 Table 8 SOC stocks (t/ha) under different land use and in different soils in various parts of the world. Location Land use, soil type Brazil — Distrito Federal Brazil — Rio Grande do Sul Tillage — 6 treatments 100 cm 3 different crop rotations in: Zero till 100 cm Conventional tillage Rotations with intercropped or cover–crop legumes in: Zero till 100 cm Conventional tillage Alfisols 30 cm Entisols Inceptisols Mollisols Oxisols Ultisols Mixed Ombrophyllous forest 30 cm Forest on Arenosol 100 cm Forest on Histosol Cropland (mainly cereals and potatoes) 100 cm Forest Grazing – 100 cm Forest 100 cm Pasture Crops (82 row crops) Forestland 100 cm Grassland Farmland Forest 50 cm Agriculture (tea, coffee, maize and banana) Brazil — Rio Grande do Sul Brazil — Rio Grande do Sul Brazil Brazil — Amazon Spain — Canalda river basin USA USA China Rwanda — Rukarara river catchment Soils under arable crops and vineyard had the lowest SOC concentration and stocks as a result of reduced organic matter input and enhanced decomposition (Elliott, 1986; Sanford, 2014; Schrumpf et al., 2013), but SOC levels could improve with careful soil management (Lal, 2006). Soil erosion may decrease SOC stocks in agricultural systems (Don et al., 2011) whereas leaving the land fallow may increase SOC levels depending on the length of the fallow. Hartemink (1998) found, in Papua New Guinea, that SOC concentration changed from 51 g C/kg to 36 g C/kg after 17 years of sugarcane cultivation. Planted forests in Vale dos Vinhedos are mostly pinus or eucalyptus, and the soils generally had a low SOC concentration and SOC stocks. It is known that coniferous and broadleaf trees can have different carbon accumulation (Guo and Gifford, 2002) but we were not able to distinguish these forest types. Planted broadleaf trees accumulate SOC levels comparable to natural forests. Soil C stocks under plantation forest could be restored to the original level under native forest, but it may requires several decades (Guo and Gifford, 2002; O'Brien and Jastrow, 2013). As planted forests are harvested there may be considerable soil erosion and loss of topsoil carbon (Hartemink, 2003). The SOC concentration and stocks differed by soil order. Until 30 cm soil depth, Entisols have a higher SOC concentration but with depth Oxisols have the highest SOC concentration. Most Entisols (58%) are under forest which explains some of the higher SOC concentrations. Oxisols are deeper soils and have possibility of long-term accumulation of SOC with depth. Many of the Oxisols are under pasture (16%), whereas other soil orders have less than 3% of their area under pasture. Pasture has generally higher SOC accumulation with depth. Alfisols are mostly under vineyard which can explain their lower SOC levels. About twothird of the Mollisols are under forest, accumulating more SOC in upper layers. Most of the Inceptisols are under forest (39%) and vineyard (35%). SOC stocks were calculated and corrected based on equivalent soil mass (Gifford and Roderick, 2003; Lee et al., 2009; Ellert and Bettany, 1995). We found corrected SOC stocks varying from 104 t C/ha in vineyards in Alfisols to 280 t C/ha in pasture areas in Oxisols, with an average of 161 t C/ha. Results of SOC stocks for 100 cm depth (Table 6, Fig. 7) are comparable to other studies (Table 8). This can be attributed to the relatively high SOC concentrations. About 16% of the SOC Depth SOC stocks (t C/ha) Reference 171 Jantalia et al. (2007) Sisti et al. (2004) 175.2 163.8 Boddey et al. (2010) 154–172 132–163 77 66 83 76 77 48 61–128 40 724 63 116 89 345 76.8 74.9 107 143.3 82.4 92.2 295–487 114–169 Tornquist et al. (2009a) Bernoux et al. (2002) Batjes and Dijkshoorn (1999) Simó et al. (2014) Wills et al. (2014) Bliss et al. (2014) Yu et al. (2007) Wasige et al. (2014) concentration values between 60 and 100 cm depth exceeded 10 g C/ kg, and considering 40 cm thickness it explains the relative high SOC stocks with depths. Environmental conditions in the study area favor SOC accumulation, due the high precipitation and relatively low temperature. SOC stocks average for soils under arable crops is 163 t C/ha, for fallow is 175 t C/ha, for pasture is 205 t C/ha, vineyard is 150 t C/ ha, for planted forest is 149 t C/ha and 184 t C/ha for soils under forest. Other studies in Brazil found similar values such the studies by Boddey et al. (2010), Sisti et al. (2004) and Jantalia et al. (2007) (Table 8). Tornquist et al. (2009a) found in Rio Grande do Sul State, for SOC stocks to 30 cm soil depth of non-sandy and non-wet soils, mean values of 77 t C/ha for Alfisols, 66 t C/ha for Entisols, 83 t C/ha for Inceptisols, 76 t C/ha for Mollisols, 77 t C/ha for Oxisols and 48 t C/ha for Ultisols. These stocks are comparable to the current study in Vale dos Vinhedos, based on equivalent soil mass, of 57 t C/ha for Alfisols, 85 t C/ha for Entisols, 76 t C/ha for Inceptisols, 60 t C/ha for Mollisols, 106 t C/ha for Oxisols and 67 t C/ha for Ultisols. Bernoux et al. (2002) found for nonsandy or non-wet soils, in areas with mixed forest, SOC stocks (0–30 cm) between 61 and 128 t C/ha. These values are comparable to 84 t C/ha found in forest areas in Vale dos Vinhedos at the same depth based on the equivalent soil mass. Wasige et al. (2014), studying SOC in Rwanda until 50 cm depth, found under forest, stocks ranged 295 t C/ha in Cambisols to 487 t C/ha in Histosols. These values were not corrected by mass and are higher than the 115 t C/ha found in Vale dos Vinhedos (Table 6), for forest until 60 cm depth, corrected by mass. For agriculture areas (main crops are tea, coffee, maize and banana), the values were between 114 t C/ha in Acrisols (Ultisols) and 169 t C/ha in Ferralsols (Oxisols). These SOC stocks are similar to found in arable crops (126.3 t C/ha) and vineyard (115 t C/ha) areas in our study up to 60 cm soil depth. 4.4. Uncertainty and probability maps It was found that 88% of validation values are within the prediction intervals. Malone et al. (2011) found similar result using an empirical uncertainty method based in distribution of prediction errors. However, for depth with higher spatial covariance of residuals (30–60 cm and 220 B.R. Bonfatti et al. / Geoderma 261 (2016) 204–221 60–100 cm) more than 90% of the values were within the prediction intervals. Our results suggest that the methodology adopted to calculate uncertainty depends of the spatial covariance of the residuals. The limited accuracy may be related to variation in environmental conditions between the training and validation data, lower spatial relation found in the most of interval depths, and errors in measures of the training or validation samples. The SOC stocks probability maps (Fig. 10) reflect SOC stocks exceeding 184 t C/ha. Such areas are found in valley bottoms due the sediment accumulation and reduced drainage, and in Entisols, Mollisols under forest because of higher production of organic material and lower rates of decomposition. The low probability values are mostly in soils under vineyard or arable crops (mainly Inceptisols and Ultisols). The maps shows that only about 13% of the area has 80% of probability for exceeding the 184 t C/ha. These areas may have the same or more SOC than the soils under original land use. The 20% probability map shows that non-colored areas have 80% of probability to be able to stock more SOC. About 42% of soils of study area (3374 ha) could sequester more carbon if occupied by natural forest. 4.5. Soil C changes The PNVSC analysis showed that the topsoils could accumulate more SOC if they were under forest (Table 7) because of increased organic material addition and reduced decomposition. Below 15 cm depth, soils under pasture have a higher capacity to accumulate SOC which is commonly found (Guo and Gifford, 2002; Lacoste et al., 2014; Nieder and Benbi, 2008). At interval depth 30–60 cm, regardless of soil type or land use, the soil accumulates more carbon than if the soil was under forest. A possible explanation is that there is storage in carbon in that depth after carbon being translocated from upper layers. 5. Conclusions From this research the following can be concluded: - Up to 30 cm soil depth the primary covariates for prediction SOC concentration were Entisols, X coordinate, DEM and Aspect. - With depth, the primary covariates for prediction SOC concentration were Overland Flow Distance, Aspect, Soil Order, Y coordinate. - For the prediction of the soil depth, the primary covariates were Soil Order and Valley Depth. - Forest accumulates more carbon in upper layers and pasture accumulates more carbon with depth. - Oxisols and Entisols accumulate larger contents of SOC. Lower values for SOC were found in Alfisols, Ultisols, arable crops, vineyard and planted forest. - The SOC stocks (down to 100 cm) were on average 166 t C/ha but varied between 107 t C/ha in vineyards on Alfisols, and 324 t C/ha in fallow areas on Oxisols. - The PNVSC analysis showed that carbon was lost when land use changes from natural environment, reducing the potential of carbon sequestration. Acknowledgments We are especially grateful to Carlos Alberto Flores, Reinaldo Oscar Pötter, Eliana Casco Sarmento, Eliseu José Weber and Heinrich Hasenack, for the soil survey in Vale dos Vinhedos and for making the data available. The first author was supported by the CAPES Foundation, Ministry of Education of Brazil (Process BEX 3095/14-2). We are grateful to Prof. Budiman Minansny of the University of Sydney who made useful comments on the draft of this paper, and to two anonymous reviewers for their suggestions that improved this paper. References Adhikari, K., Hartemink, A.E., 2015. Digital mapping of topsoil carbon content and changes in the Driftless Area of Wisconsin, USA. Soil Sci. Soc. Am. J. 79, 155–164. http://dx.doi. org/10.2136/sssaj2014.09.0392. Adhikari, K., Hartemink, A.E., Minasny, B., Bou Kheir, R., Greve, M.B., Greve, M.H., 2014. Digital mapping of soil organic carbon contents and stocks in Denmark. 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