1 Introduction

Soil being a vital part of our ecosystem forms a substratum for sustaining life on the Earth. It is estimated that about 75% of total carbonic stock of terrestrial ecosystem lies in soil. The carbon content in soil is most important parameter for examining soil quality and soil health (Brown 1997). Forest Inventory and Analysis (FIA) with its baseline regional carbon assessment reports have helped researchers to understand about carbon content and harvested wood products in forest ecosystems (Gullison et al. 2007; Wu et al. 2009; Houghton et al. 2009). The information about the relationship among the carbon storage, past management, and disturbance impacts can be retrieved from the varied trends of the carbon stocks along with the companion assessments on forest carbon disturbances (Tekin et al. 2012). This associated information can be used to assess the short- and long-term carbon consequences for alternative forest strategies. The climate change and global warming have created severe negative inferences to environment all over world. Carbon dioxide alone supplies about 60% of the total worldwide warming and plays an important role in carbon sequestration. “Soil organic carbon (SOC),” which is a part of natural carbon cycle—the quantity of carbon stored in the soil—is a constituent of soil organic matter, produced by disintegration of plant and animal materials at various stages in soil (Barnes et al. 2003; Gao and Goetz 1990; McBratney et al. 2003). Soil organic matter constitutes humus, faunal, and microbial biomass dissolved organic matter and carbonized organic matter. It releases the nutrients for plant progress, encourages the structural, biological, and physical health of the soil, and is a buffer against the human elements (Maynard et al. 2007). Soil organic organisms are important for the protection of flora and are sources of the nutrients for the plants. SOC is one of the most significant elements of the soil due to its ability to influence plant development as both a source of energy and a trigger for nutrient accessibility through mineralization (Selige et al. 2006). Soil organic carbon behaves both as a sink and as a source of atmospheric carbon and is the largest vigorous terrestrial carbon reservoir. Thus, pool of soil organic carbon is significant in climate alteration processes by acting as a basis of sinks for atmospheric CO2.

The amount of soil carbon present in soil can vary according to the landscape types and paddock over the time depending on climate (temperature and rainfall), slope, farming methods, land management, soil nutrition, and soil type (Neigh et al. 2014). Soil organic carbon can be assessed and predicted using different vegetation indices like Brightness Index, Greenness Index, NDVI, SAVI/MSAVI, Wetness Index, and Compound Topographic Index as the parameters for the model with the help of band-rationing algorithm and surveyed data (Gupta et al. 2014; Pandey et al. 2014). The traditional method of acquiring data through field is time consuming and involves huge investment. Geospatial techniques, on the other hand, being cost-effective and having synoptic view, can be utilized for predicting SOC through model building. The present study makes an integrated use of remote sensing data, laboratory data, geostatistical tools, and field data for predicting SOC in Sariska Tiger Reserve in India (Zheng et al. 2004).

2 Materials and methods

2.1 Study area

Sariska Tiger Reserve is a tiger reserve situated in the Alwar district of Rajasthan, India. The landscape of the tiger reserve contains dry deciduous forests, scrub–thorn arid forests, rocks, grasses, and hilly cliffs (Jain and Sajjad 2016a, b). Vegetation of the study area can be classified in two major types, i.e., tropical dry deciduous forest- and tropical thorn forest-based structural attributes (Jain and Sajjad 2016a, b). In terms of the succession, and concept of continuum of vegetation, the large-scale formations in the area are Acacia catechu and Anogeissu spendula vegetation types (Jain et al. 2016; Kumar et al. 2015). Dhok (Anogeissus pendula Edgew.) is the main species of the tree covering over 90% of the area. It is associated with species like Salar (Boswellia serrata Planch.) and Urjan (Linnea corommrndelica Houtt.) which are small trees, with a short usually crooked bole which grow on rocks and dry area. It extends from the Aravalli hills in Rajputana to Bundelkhand and is important tree, not only as a source of timber and fuel but also for clothing dry tracts. Khair (Acacia catechu Willd.) and Bamboo (Dendro calamusstrictus Roxb.) is small- or medium-sized deciduous tree attaining a height of 12–15 m with light feathery crown, the branch let armed with paired and re-curved spines. The study area was divided into square plots of 0.1 hectare, and a total of 30 soil samples were composed from the whole research area (Fig. 1). Measurement of various parameters like species name, height, diameter at breast height (DBH) for all sampled tropical forest trees above 10 cm DBH was carried out.

Fig. 1
figure 1

Location map of study area

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2.2 Data used

The study utilized satellite, field, and laboratory data. Base map was prepared using Survey of India (SOI) toposheet (1:50,000). Sentinel-2A Multispectral Instrument (MSI) sensor satellite images were for used for predicting soil carbon. The satellite functions in a sun synchronous orbit with a 10-day repeat cycle. Specific bands like 2, 3, 4, 8, and 11 (Blue, Green, Red, NIR and SWIR respectively) with 10 m spatial resolution were used. Sentinel-2A Multi Spectral Instrument (MSI) contains 13 spectral bands ranging from visible to short-wave infrared (SWIR) wavelengths along a 180° phase orbit with 290-km orbital swath. Measurement of sampled trees was carried out in field, and soil parameters were tested in the laboratory.

2.3 The predictor variables (NDVI, SAVI, and RDVI)

NDVI, RDVI, and SAVI were derived using blue, green, red, and near-infrared bands of the satellite data to assess the biophysical status of surrounding soil (Kumar et al. 2016; Tomar et al. 2013). The NDVI is a modest graphical indicator that can be used to define the greenness, the relative density, and healthiness of vegetation (Powell et al. 2010). This is calculated using Eq. 1. Red band has maximum absorption by the leaf pigments, and infrared band has maximum reflectance due to leaf cellular structure.

$$ {\text{NDVI}} = \frac{{R_{\text{NIR}} - R_{\text{RED}} }}{{R_{\text{NIR}} + R_{\text{RED}} }} $$
(1)

SAVI or Modified Soil Adjusted Vegetation Index (MSAVI) is approximately similar to NDVI, but MSAVI diminishes the consequence of bare soil on the SAVI (Richardson and Wiegand 1977; Huete 1988). It is calculated by using Eq. 2 (Qi et al. 1994).

$$ {\text{MSAVI}} = \frac{1}{2}\left\{ {2\left( {R_{\text{NIR}} + 1} \right) - \sqrt {(2*R_{\text{NIR}} + 1)^{2} - 8\left( {R_{\text{NIR}} - R_{\text{RED}} } \right)} } \right\}. $$
(2)

RDVI is generally used to analyze the vegetation at growth stage and the amount of greenness present in the vegetation. RDVI was calculated using the following equation:

$$ {\text{RDVI}} = \frac{{(R_{\text{NIR}} - R_{\text{RED}} )}}{{\sqrt {R_{\text{NIR}} + R_{\text{RED}} } }} $$
(3)

2.4 Soil carbon analysis from field data

Walkey–Black procedure was followed for estimating soil organic carbon at 5 cm depth of soil, where the sampler radius is 3.8 cm and sampler volume is 226.8229 cm3. Bulk density (g/cm3) and soil carbon content (%) were calculated from the soil data collected from 30 locations in the study area (Table 1). Bulk density is determined using Eq. (4) (Vagen and Winowiecki 2013; Grossman and Reinsch 2002). We applied drying procedure and baked soil carbon content at 900 °C using an NC-Analyzer Model Sumigraph-NC 90A. Soil carbon and bulk density are calculated by using Eqs. 4 and 5:

$$ {\text{Bulk}}\,{\text{density}}\left( {{\text{g}}/{\text{cm}}^{3} } \right) = \frac{{{\text{Mass}}\,{\text{of}}\,{\text{oven}} - {\text{dried}}\,{\text{soil}}}}{{{\text{Total}}\,{\text{volume}}}}, $$
(4)
$$ {\text{Soil}}\,{\text{carbon}}\left( {{\text{t}}/{\text{ph}}} \right) = {\text{Soil}}\,{\text{depth}}*{\text{soil}}\,{\text{bulk}}\,{\text{density}}*{\text{carbon}}\,{\text{content}}\,\left( {\text{\% }} \right). $$
(5)
Table 1 Summary of field sampling in Sariska Tiger Reserve
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2.5 Assessing relation between SOC and LAI

SOC is found in soil as a constituent of various biochemical multiplexes. Thus, SOC having such biochemical cannot be extracted from the satellite data. In order to delineate SOC through remote sensing, a constraint (terrestrial surface reflectance) has to be linked SOC, which would represent a strong correlation among them. Leaf area index was derived using Landsat 8, and OLI image was used for delineating SOC through spectral characteristic.

LAIsatellite was calculated in two successive processes. Firstly, the soil fraction (F C) covered by plants was calculated using equation via (Choudhury et al. 1994).

$$ F_{\text{C}} = \left( {\frac{{{\text{NDVI}}_{ \hbox{max} } - {\text{NDVI}}}}{{{\text{NDVI}}_{ \hbox{max} } - {\text{NIDVI}}_{ \hbox{min} } }}} \right). $$
(6)

Again on 1998, Campbell and Normann stated the soil fraction index using LAI, as mentioned below (Eq. 6). So LAI can be derived by simplifying Eqs. (7) and (8)

$$ F_{\text{C}} = {\text{exp }}\left( { - K_{\text{be}} \left( 0 \right)*{\text{LAI}}} \right), $$
(7)

F C = soil fraction covered by plants of given pixel; K be(0) = spherical leaf angle distribution = 0.5 (standard)

So, leaf area index can be simplified as;

$$ {\text{LAI}}_{\text{satellite}} = - 2{\text{Ln}}\left( {1 - F_{\text{C}} } \right). $$
(8)

The spectral linear relationship between LAI and SOC was evaluated through linear regression analysis.

2.6 SOC extraction using Kriging method

Location points of SOC were interpolated using Kriging method (Oliver 1990). This method weights the neighboring dignified values and provides an estimate for an unmeasured plot location. The statistical values for autocorrelation models were calculated through variograms and covariance functions. The model predicts the unknown values after autocorrelation of the data. Prediction value for unmeasured location is calculated by using Eq. 9:

$$ Z\left( {s_{O} } \right) = \mathop \sum \limits_{i = 1}^{N} \lambda_{i} Z\left( {S_{i} } \right) $$
(9)

\( Z\left( {s_{O} } \right) \) = prediction value for unmeasured location; Z(S i ) = ith location by measured value; λ i  = ith location by an unidentified weight for the estimated value; N = the number of measured value

2.7 Model validation

Observed (y) and predicted as (\( \hat{y} \)) values were divided into two groups for each land-cover type (Black 1965). The ground measured SOC was taken as the observed variable and the SOC extracted from satellite data as the predictors. The results were validated by comparing the (root-mean-square error (RMSE) as well as absolute RMSE (Eq. 10).

$$ {\text{RMSE}} = \sqrt {\frac{{\left( {\check{Y} - Y} \right)^{2} }}{N}} $$
(10)

3 Result and discussion

3.1 Predictor variable

NDVI (Fig. 2a) for the study area ranges from − 0.41 to + 0.43. Features like barren rock, sand, or snow displayed very low NDVI values (0.1 or less) (Kumar et al. 2014). Scarce vegetation such as bushes and grasslands or crops showed moderate NDVI values (approximately 0.2–0.5). Similarly SAVI (Fig. 2b) is also a kind of vegetation index which is used for enhancing vegetation brightness in low-vegetation canopy areas using background adjustment factor. SAVI values for the study area varied from -0.6 to 0.63. The value beyond 0.2 indicated diminishing of the soil brightness (Kumar et al. 2013; Tomar et al. 2014).

Fig. 2
figure 2

Mapping of predictor variables using remote sensing data: a Normalized Vegetation Index, b Soil Adjusted Vegetation Index, c Renormalized Vegetation Index

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3.2 Analysis of SOC using field data

A summary of the carbon stocks for the whole part of research area is shown in Table 1. The range of SOC stock varies from 1.90 to 26.55 t/ha in the study area. SOC is mostly found in the core zone of tiger reserve area, where as lowest values are found all around the border of the study area.

3.3 Analysis of LAI and SOC relationship

The soil fraction value (Fig. 3a) for the study area ranges from − 0.01 to + 1.00. The value beyond + 0.1 is for those soil surfaces which are covered by the plants. LAI (Fig. 3b) varied from − 0.91 to + 0.56 m. Low LAI found in the study area is associated with the texture of sandy soil. The LAI variation was found to be caused by altered management practices. The effect of biophysical factors on LAI was found to be almost identical in the entire study area.

Fig. 3
figure 3

a Soil surface fraction and b leaf area index

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A regression investigation was accomplished between SOC (predicted and field data) and LAI to explore their relationship. We performed regression analysis twice: first between predicted SOC and LAI, and second between LAI and field SOC data. The coefficient of regression (R 2) was resulted to 95% for the first case (Fig. 4a) and 79% for the second case (Fig. 4b). The analysis revealed that significant correlation was found between predicted SOC and LAI, as p value is less than 0.05 (0.032 < 0.005). So LAI can be used as a constraint for extracting SOC using remote sensing.

Fig. 4
figure 4

a Regression analysis between SOC (predicted) and LAI. b Regression analysis between SOC (observed) and LAI

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3.4 SOC prediction

The SOC map generated from Kriging model using Landsat OLI data clearly shows variation in the SOC stocks. The map showed spatially interpolated SOC stocks and helped in assessing the complexity of SOC storage in the Sariska Tiger Reserve. It is observed that the stock decreases with the increasing slope. Among the various categories of land-use/land-cover, vegetation has the maximum content of carbon stock, followed by the agricultural, fallow lands, and is very low at the settlement. Vegetation has a higher stock of SOC due to healthy vegetation that gives a steady supply of organic matter to the stock after decomposition. Fallow lands are open lands with little shrub bery, so they have greater stock than settlements. SOC stock and its spatial distribution is shown in Fig. 5. The interpolated the value for the entire study area ranges from 0.273 to 19.064 t/ha.

Fig. 5
figure 5

Predicted soil organic carbon stock at Sariska Tiger Reserve

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3.5 Validation of results

The RMSE is calculated using Eq. 10 where in \( \check{Y} \) was taken as predicted SOC and Y as observed SOC from the field data. The model accuracy was found to be 0.89. Kriging method has given an acceptable result in this study due to the collection of more number of predictors (sampling) for this model. A positive and strong affiliation was found between the SOC (Predicted from the satellite image) and leaf area index (LAIsatellite). Regression analysis revealed strong relationship between the leaf area index and predicted SOC. Spectral reflectance of soil organic carbon with multiplex biochemical cannot be measured precisely and there fore cannot be monitored directly using remote sensing data.

4 Conclusion

The study predicted soil organic carbon distribution using field inventory data in Sariska Tiger Reserve, India. The distribution of carbon stock across the reserve was modeled by Kriging geospatial interpolation technique using Landsat 8 OLI data. We predicted SOC using leaf area index derived through satellite data. LAI can be significantly used as a good constraint for calculating SOC, as the regression for the LAIsatellite and SOC (predicted) was found to be R 2 = 0.95, with p value less than 0.05. Spatial distribution of SOC shows that forest has maximum stock followed by agricultural lands, while built-up area has the lowest stock. The findings further revealed low SOC concentration along steep slopes. Prediction of soil organic carbon may help in efficient management of forest. Higher-resolution satellite data and Kriging algorithm for soil characteristic can provide accurate information for monitoring health of tree species in different geographical regions at various scales.