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Comparison of GIS-based interpolation methods for spatial distribution of soil
organic carbon (SOC)
Gouri Sankar Bhunia, Pravat Kumar shit, Ramkrishna Maiti
PII: S1658-077X(15)30082-5
DOI: http://dx.doi.org/10.1016/j.jssas.2016.02.001
Reference: JSSAS 203
To appear in: Journal of the Saudi Society of Agricultural Sciences
Received Date: 17 October 2015
Revised Date: 31 January 2016
Accepted Date: 7 February 2016
Please cite this article as: Bhunia, G.S., shit, P.K., Maiti, R., Comparison of GIS-based interpolation methods for
spatial distribution of soil organic carbon (SOC), Journal of the Saudi Society of Agricultural Sciences (2016), doi:
http://dx.doi.org/10.1016/j.jssas.2016.02.001
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Comparison of GIS-based spatial
distribution of soil organic carbon (SOC)
Gouri Sankar Bhunia1, Pravat Kumar shit2 & Ramkrishna Maiti3
1Bihar Remote Sensing Application Center, IGSC-Planetarium, Adalatganj, Bailey Road, Patna-800001,
Bihar, India
2-721102, West Bengal,
India.
3Dept. of Geography and Environment Management, Vidyasagar University, Medinipur-721102, West
Bengal, India
Comparison of GIS-based spatial
distribution of soil organic carbon (SOC)
Abstract
The ecological, economical, and agricultural benefits of accurate interpolation of spatial
distribution patterns of soil organic carbon (SOC) are well recognized. In the present study,
different interpolation techniques in a geographical information system (GIS) environment are
analyzed and compared for estimating the spatial variation of SOC at three different soil depth
(0-20cm, 20-40 cm and 40-100 cm) in Medinipur Block, West Bengal, India. Stratified random
samples of total 98 soils were collated from different landuse sites including agriculture,
scrubland, forest, grassland, and fallow land of the study area. A portable global positioning
system (GPS) was used to collect coordinates of each sample site. Five interpolation methods
like IDW (inverse distance weighting), LPI (local polynomial interpolation), RBF (radial basis
function), OK (ordinary kriging) and EBK (Empirical Bayes kriging) are used to generate spatial
distribution of SOC. SOC are concentrated in forest land and less SOC are observed in bare land.
The cross validation is applied to evaluate the accuracy of interpolation methods through
coefficient of determination (R2) and root mean square error (RMSE). The results indicate that
OK is superior method with the least RMSE and highest R2 value for interpolation of SOC
spatial distribution.
Keywords: Soil organic carbon; Deterministic interpolation; Geostatistical interpolation; spatial
variation
1. Introduction
Spatial variability of soil organic carbon (SOC) is an important indicator of soil quality, as well
as carbon pools in the terrestrial ecosystem important in ecological modeling,
environmental prediction, precision agriculture, and natural resources management (Wei et al.,
2008, Zhang et al., 2012, Liu et al., 2014). Revealing spatial pattern
will provide the basis for evaluating soil fertility, and assist in the development of sound
environmental management policies for agriculture. Scientific management of SOC nutrient is
important for its sustainable development in agricultural system. So, there is a need of adequate
information about spatio-temporal behavior of SOC over a region. SOC measurements, however,
are inherently expensive and time consuming, particularly during the installation phase, which
requires soil sampling. Consequently, the number of soil sampling that is available in a given
area is often relatively sparse and does not reflect the actual level of variation that may be
present. Therefore, accurate interpolation of SOC at unsampled locations is needed for better
planning and management.
Different statistical and geostatistical approaches have been used in the past to estimate the
spatial distribution of SOC (Kumar et al., 2012; 2013). Classical statistics could not make out the
spatial allocation of soil properties at the unsampled locations. Geostatistics is an efficient
method for study of spatial allocation of soil characteristics and their inconsistency and reducing
the variance of assessment error and execution costs (Saito et al., 2005; Liu et al., 2014; Behera
and Shukla, 2015). Earlier researchers have applied geospatial techniques to appraise spatial
association in soils and to evaluate the geographical changeability of soil characteristics (Wei et
al., 2008). Zare-mehrjardi et al., (2010), reported that ordinary kriging (OK) and cokriging
methods were better than inverse distance weighting (IDW) method for prediction of the spatial
distribution of soil properties. Robinson and Metternicht (2006) used three different techniques
including kriging, IDW and RBF (Radial basis function) for prediction of the levels of the soil
salinity, acidity and organic matter. Pang et al., (2011) reported that ordinary kriging is most
common type of kriging in practice and provides an estimate of surface maps of soil properties.
Hussain et al. (2014) reported that empirical bayes kriging (EBK) are most suitable for spatial
prediction of total dissolved solids (TSD) in drinking water. Mirzaei and Sakizadeh (2015)
reported that EBK model is best other than geostatistical models such as OK and IDW for
estimation of groundwater contamination.
These five widely used interpolation methods (RBF, IDW, OK, LPI and EBK models) have led
to the quest about which is most appropriate in prediction of soil organic carbon in deferent soil
depth. Therefore, the objective of this study is to conduct a thorough comparison of the GIS
based interpolation techniques for estimating the spatial distribution of SOC in Medinipur Block,
West Bengal, India and apply cross validation to evaluate the accuracy of interpolation method
through the root mean square error (RMSE) measurement.
2. Materials and methods
2.1. Study area
The study was conducted in Medinipur block
--
E longitude covering an area of 353 sq km (Fig. 1). The area is dry and the land surface of the
block is characterized by red lateritic covered area, flat alluvial and deltaic plains. Extremely
rugged topography is seen in the western part of the block and rolling topography is experienced
in lateritic covered area (Shit et al., 2013). The maximum temperature recorded in April is 43
degree centigrade and minimum temperature is 9 degree centigrade. The average annual rainfall
is about 1450 mm. Number of rainy days per annum is near about 101 days.
2.2. Sampling and estimate of soil properties
A pilot study was conducted to analyse the soil particles under different land use characteristics.
Reconnaissance soil survey of Medinipur Block was carried out on 1:50,000 scale during 2014-
2015 using the Survey of India (SOI) Toposheets as base maps. The Geo-coded Landsat 4-5
Thematic Mapper (TM) false colour composite images were visually and digitally interpreted for
physiographic analysis. Land use map was generated based on supervised classification
technique using maximum liklihood algorithm technique in ERDAS Imagine software v9.0. The
entire block has been classified into eight classes following the forest, fallow land, scrub land,
agricultural land, river, sand and settlement area. To validate the classification accuracy, an error
matrix table was generated and accuracy assessment analysis was performed .The study of soil
profile in all physiographic units was done under different land use to develop soil-physiography
relationship. Using the base maps, the field survey was carried out following the procedure as
outlined in the soil survey manual (1970). The morphological features of representative pedons
in each physiographic unit were studies upto a depth of 100 cm (shallow soils) and the soil
samples were collected from different soil horizons for laboratory analysis.
Stratified random sampling technique was used for sampling in field during post-monsoon
season. A total 98 soil samples were collated from 36 sites including agriculture (21), scrubland
(16), forest (19), grassland (16), and fallow land (16) of the Medinipur block. A portable global
positioning system (GPS) was used to record each sample site. In forest land use, the sampling
was conducted in dense forest, degraded forest and open forest area. Undisturbed soil samples at
three depths of 0-20 cm, 20-40 cm, and 40100 cm were collected with 5 soil cores from each
site and mixed well into a composite soil sample. Soil samples were air dried and passed through
a 2 mm sieve for laboratory analysis of soil texture and SOC was measured by Walkely-Black
wet oxidation method (Bao 2000).
2.3. Interpolation methods
In the present study, deterministic (i.e., create surfaces from measured points) and geostatistical
(i.e., utilize the statistical properties of the measured points) interpolation techniques were used.
In this study, a variety of deterministic interpolation techniques, including those based on either
the extent of similarity (inverse distance weighted), local polynomial interpolation (LPI), degree
of smoothing (radial basis functions) and geostatistical interpolation, namely ordinary kriging
(OK), and Empirical Bayes (EBK) were used to generate the spatial distribution of SOC
(Johnston et al., 2001).
2.3.1. IDW method
The IDW is one of the mostly applied and deterministic interpolation techniques in the field of
soil science. IDW estimates were made based on nearby known locations. The weights assigned
to the interpolating points are the inverse of its distance from the interpolation point.
Consequently, the close points are made-up to have more weights (so, more impact) than distant
points and vice versa. The known sample points are implicit to be self-governing from each other
(Robinson and Metternicht, 2006).
1
0
1
() 1
ni
iij
n
iij
x
h
Zx
h
(1)
Where, z (x0) is the interpolated value, n representing the total number of sample data values, xi
is the ith data value, hij is the separation distance between interpolated value and the sample data
value, and ß denotes the weighting power:
2.3.2. LPI method
LPI fits the local polynomial using points only within the specified neighbourhood instead of all
the data (Hani and Abari, 2011). Then the neighbourhoods can overlap, and the surface value at
the centre of the neighbourhood is estimated as the predicted value. LPI is capable of producing
surfaces that capture the short range variation (ESRI, 2001).
2.3.3. RBF method
Radial Basis Function (RBF) predicts values identical with those measured at the same point and
the generated surface requires passing through each measured points. The predicted values can
vary above the maximum or below the minimum of the measured values (Li et al., 2007, 2011).
RBF method is a family of five deterministic exact interpolation techniques: thin-plate spline
(TPS), spline with tension (SPT), completely regularised spline (CRS), multi-quadratic function
(MQ and inverse multi-quadratic function (IMQ). RBF fits a surface through the measured
sample values while minimizing the total curvature of the surface (Johnston et al., 2001). RBF is
ineffective when there is a dramatic change in the surface values within short distances (ESRI,
2001, Cheng and Xie 2009.). The most widely used RBF that is CRS was selected in this study.
2.3.4. OK method
Ordinary Kriging method incorporates statistical properties of the measured data (spatial
autocorrelation). The Kriging approach uses the semivariogram to express the spatial continuity
(autocorrelation). The semivariogram measures the strength of the statistical correlation as a
function of distance. The range is the distance at which the spatial correlation vanishes, and the
sill corresponds to the maximum variability in the absence of spatial dependence. The coefficient
of determination (R2) was employed to determine goodness of fit (Robertson 2008). Kriging
estimate z*(x0) and error estimation variance k2(x0) at any point x0 were, respectively,
calculated as follows:
01
*( ) ( )
n
ii
i
Z x z x
(2)
200
1
( ) ( )
n
k i i
i
x x x
(3)
Where, i are the weights; μ is the lagrange constant; and γ(x0−xi) is the semivariogram value
corresponding to the distance between x0 and xi (Vauclin et.al. 1983; Agrawal et. al. 1995).
Semivariograms were used as the basic tool with which to examine the spatial distribution
structure of the soil properties. Based on the regionalized variable theory and intrinsic
hypotheses (Nielsen and Wendroth 2003), a semivariogram is expressed as:
() 2
1
1
( ) [ ( ) ( )]
2 ( )
Nh
ii
i
h Z x Z x h
Nh
(4)
where parameter of the soil property, N(h)
is the number of pairs of locations separated by a lag distance h, Z (xi), and Z (xi + h) are values
of Z at positions xi and xi + h (Wang and Shao 2013). The empirical semivariograms obtained
from the data were fitted by theoretical semivariogram models to produce geostatistical
parameters, including nugget variance (C0), structured variance (C1), sill variance (C0+C1), and
The nugget/sill ratio, C0/(C0+C1),was calculated to characterize the
spatial dependency of the values. In general, a nugget/sill ratio <25 % indicates strong spatial
dependency and >75 % indicates weak spatial dependency; otherwise, the spatial dependency is
moderate (Cambardella et al. 1994).
2.3.5. Empirical Bayesian kriging (EBK) Method
Empirical Bayesian kriging automates the most difficult aspects through a process of sub setting
and simulations. EBK process implicitly assumes that the estimated semivariogram is the true
semivariogram for the interpolation region and a linear prediction that incorporates variable
spatial damping. The result is a robust non-stationary algorithm for spatial interpolating
geophysical corrections. This algorithm extends local trends when data coverage is good and
allows for bending to a priori background mean when data coverage is poor (Knotters et al.,
2010; Krivoruchko, 2012; Krivoruchko and Butler 2013).
2.4. Cross-validation
Cross-validation technique was adopted for evaluating and comparing the performance of
different interpolation methods. The sample points were arbitrarily divided into two datasets,
with one used to train a model and the other used to validate the model. To reduce variability, the
training and validation sets must cross-over in successive rounds such that each data point is able
to be validated against. The mean error (ME), the mean relative error (MRE) and the root mean
square error (RMSE) for error measurement and coefficient of determination (R2 value) were
estimated to evaluate the accuracy of interpolation methods. MRE is an important measure since
both RMSE and ME do not provide a relative indication in reference to the actual data.
2
1(0 )
N
ii
iS
RMSE N
(5)
10
N
ii
iS
ME N
(6)
RMSE
MRE
(7)
Where, 0i is observed value and Si is the predicted value, N is the Number of samples,
range and equals the difference between the maximum and minimum observed data.
3. Results and discussion
3.1. Land use land cover (LULC)
Land use characteristics of the study site have been categorized into eight classes (Fig.1).
Agricultural land covers 56.91% (201 km2) of the study area and 24.76% (87 km2) area is
covered by dense, degraded and open forest land. Consequently, the fallow land is covered by
8.58% (30 km2) and settlement area is enclosed by 3.57% (12 km2) of the entire study site. On
the southern part of the study site Kangsaboti river is flowing from western to eastern direction
covering an area of 1.17% (4 km2) of the study site and the river bed deposit of sand covers an
enclosed area of 2.48 km2 (0.70%). The grassland covers 4.31% (15 km2) of the total land. Table
2 identified the error matrix of LULC image derived from the supervised classification
technique. The overall classification accuracy and Kappa statistics were 88.00% and 0.85,
respectively.
3.2. Spatial variation of SOC
The Figure 2 represents the distribution of SOC at 0 20 cm (dark shed), 20 40 cm (dark to
gray shed) and 40 100 cm (very light grey shed) depth analysis. The result showed
concentration of SOC is maximum in agricultural land at 0 20 cm depth and the minimum
percent was recorded in fallow land and forest (Fig 2). Consequently, SOC percent was higher in
forest and agricultural land at 20 40 cm depth and minimum percent was observed in shurbs.
Results also showed the highest percent of SOC in forest and grass land at 40 100 cm depth
and lowest percent was observed in fallow land and agricultural land. The storage capacity of
carbon among the entire forest category under consideration was significantly higher in the top
layer (P<0.03). The present result is corroborated with previous studies by Gurumurthy et al
(2009); Sheikh et al (2011) and Saha et al (2012).
3.3.Vertical distribution of SOC
The vertical distribution of SOC percent was analyzed (Table 2). The average value of SOC was
0.50 at 0 20 cm depth, and the percent decreased with the increase of depth (Table 2). The
skewness and kurtosis coefficients are often used to describe the shape and flatness of data
distribution respectively. All the data showed positive skewness, showing the concentration at
lower end of data distribution. SOC content ranged from 0.02 to 0.82% (0 20 cm depth) and
the allocation was positively skewed due to few high values found in the western part of the area.
Average SOC content was 0.47 % and 0.43 % at 20 40 cm and 40 100 cm depth respectively.
The results also showed positive skewness. Briefly, a good concentration of carbon sink was
found in the 0-40 cm depth in all the forest soil samples in the study site. Storage of SOC in
upper soil layer has been associated with the growth of root systems (Pillon, 2000) and with the
quantity of above ground biomass addition on the soil surface (Burle et al., 2005) indicating that
the trees will usually increase organic carbon.
In this study, IDW, LPI, OK, EBK and RBF were used to estimate the spatial distribution of
SOC. The summary statistics of the interpolation were represented in Table 3. Figure 3
represents of spatial distribution of SOC at three difference soil depth. The characteristics of the
semivariograms for SOC are abridged in Table 4. Preliminary calculations showed that all
semivariograms were exponential. Semivariograms analysis indicated that SOC was best fitted to
exponential model with nugget, sill, and nugget/sill equal to 0.15, 1.10, and 0.14, respectively for
0 20 cm depth. The value of nugget, sill, and nugget/sill was recorded as 0.001, 0.97 and 0.10
and respectively for 20 40 cm; 0.001, 1.08 and 9.26 for 40 100 cm soil depth respectively.
3.4. Comparison of deterministic methods
Spatial distributions of SOC were analyzed in the study area obtained by deterministic methods
(IDW, LPI, and RBF). The comparative results showed LPI is more accurate than the other two
methods. The R2 value for LPI varied from 0.792, 0.816 and 0.851 for 0 20 cm, 20 40 cm and
40 100 cm respectively. The R2 value for IDW varied from 0.776, 0.791, and 0.808 and for 0
20 cm, 20 40 cm and 40 100 cm respectively. However, the value of RBF showed lesser
accuracy in the estimation method.
Most quantitative comparison of these three techniques was obtained through cross-validation
statistics (Table 3). LPI showed RMSE of 0.125, 0.121, and 0.145 at 0 20 cm, 20 40 cm and
40 100 cm soil depth respectively. IDW resulted RMSE of 0.121 0.145 whereas RBF gave
RMSE of 0.147 0.176 at different depth of SOC concentration. IDW resulted in ME of 0.385
0.645 whereas LPI gave ME of 0.257 0.468. LPI resulted in MAE of 0.216 0.251 and IDW
gave RSS of 0.210 0.254. However, the result of the analysis represented that LPI is more
accurate than IDW with lesser ME and smaller RMSE value. The analysis also showed IDW
providing better result than RBF.
3.5. Comparison of geostatistical methods
The ordinary kriging (OK) and Empirical Bayes model (EBK) are used to interpolate the spatial
variability of SOC in three soil depth (Table 3). The summary results processed by OK showed
the smallest RMSE value of 0.148, 0.120 and 0.123 at 0 20 cm, 20 40 cm and 40 100 cm
soil depth respectively. The Coefficient of determination (R2) of the model represented as 0.918,
0.921 and 0.938 at 0 20 cm, 20 40 cm and 40 100 cm soil depth respectively. Table 4
represented the key parameters of semivariogram model for OK.
The R2 of the model at each soil depth were greater than 0.5, indicating a good fit with the
ground value. OK resulted in RMSE 0.110 - 0.123 whereas EBK gave 0.127 0.131. The RSS
were approximately close to zero for all soil depths and determined that theoretical models of
SOC well reflect the spatial distribution and also corresponded strongly to the spatial correlation.
OK showed the ME of 0.110 - 0.124 whereas EBK gave 0.351 0.364. The best results, in terms
of cross validation, are achieved by OK which gave the lowest RMSE, ME and MAE. The
information derived from semivariograms pointed out the reality of different spatial dependence
for collected soil properties from the field (Table 4). The proportion of nugget to sill (C0/C0 + C)
imitates the spatial autocorrelation (Wei et al., 2008).
3.6. Comparison of geostatistical and deterministic methods
The best models from the deterministic and geostatistical methods were compared to find the
most suitable spatial interpolation method of the region. Assessment measures of model
performance are summarized in Table 3. The superiority of IDW, LPI, OK and EBK models over
RBF to predict SOC at three different soil depths was well established. To quantify the relative
performance, the percentage improvement of IDW, LPI, OK and EBK over RBF was also
calculated. The obtained results are shown in Table 5 and it was clear indicated that IDW, LPI,
OK and EB average decreased RMSE value of 18.08, 15.65, 26.12 and 19.93% respectively
lower than RBF. Similarity of the reduction of MRE value of IDW, LPI, OK and EB was 18.63,
16.51, 39.19 and 14.18 % respectively. The R2 value of IDW, LPI, OK and EBK models showed
that increased 3.81, 6.45, 21.40, and 14.63 % over RBF model.
High value of coefficients of determination, and low value of RMSE and ME indicated a good
match between observed and predicted SOC concentration at three different soil depths. The OK
gave the lowest error (RMSE value) and highest R2 value in the spatial interpolation of three soil
depth among all geostatistical methods. IDW and LPI methods gave the best results among the
deterministic methods. Overall the performance of the geostistical methods was thoroughly
compared with the deterministic methods. The ordinary kriging was found the best among all of
the methods. OK and related geostatistical techniques incorporate spatial autocorrelation and
statistically optimize the weights. OK methods often give better interpolation for estimating
values at unmeasured locations (Burgess and Webster 1980; Liu et al. 2006; Nayanaka et al.
2010, Mousavifard et al. 2012, Varouchakis and Hristopulos 2013, Venteris et al. 2014, Tripathi
et al. 2015). Among the five interpolation methods, the performance of OK was best in
comparison to other interpolation models. The MRE, which provided relative error of the
predicted data in reference to the actual data, was also very low for OK.
4. Conclusion
The clear understanding of SOC distribution is the key issue for agricultural and environment
management. Due to relative profusion of a variety of methods, many algorithms are presently
applied, and research continues, a delineation of
spatial distribution of SOC. The methods are evaluated using efficiency and error estimates of
interpolation techniques. The efficiency is assessed by coefficient of determination (R2 value),
and errors are represented by the root mean square error (RMSE), mean error (ME) and mean
relative error (MRE). The study shows that OK interpolation method is superior other than
geostistical and deterministic methods. The performance of the exponential semi-variogram
model is outstanding with OK interpolation techniques. IDW skill has the worst presentations,
deriving higher RMSE and MRE than other deterministic and geostatistical methods. The study
carries out at only 36 soils sampling sites over the study area 353 km2. The interpolation could be
more accurate, with more close samples and incorporation of sufficient topographical
information. Finally, the results guide to the amplification of trustworthy SOC concentration
maps which can significantly contribute to proper application of agricultural and ecological
modeling.
Acknowledgements
We extend our thanks to the Department of Geography and Environment Management,
Vidyasagar University, Medinipur-721102, India for providing necessary facilities for
conducting the research work. And also thank to Rahaman Agri Clinic and Agri Business Center,
Daspur (Paschim Medinipur) for providing necessary laboratory facilities for soil test.
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Figure 1 Location of the study area and sampling design with land use land cover of Medinipur
block derived from Landsat Thematic Mapper data.
Figure 2 Characteristics of Soil Organic carbon in different land use categories. The error bars
represent ± one standard error.
Figure 3 (a) Spatial distribution of SOC using IDW (inverse distance weighting)
Figure 3 (b) Spatial distribution of SOC using LPI (local polynomial interpolation)
Figure 3 (c) Spatial distribution of SOC using BRF model (radial basis function)
Figure 3 (d) Spatial distribution of SOC using EBK (Emperical Bayesian Kriging)
Figure 3 (e) Spatial distribution of SOC using OK (ordinary kriging)
Table 1 Land Use and Land Cover (LULC)
Class Name
Number
of
Pixels
Area
(in km2)
Percent
Producer
accuracy
User
accuracy
Kappa^
Built up area
14016
12.61
3.57
80.00%
100.00%
1.00
River/ water
bodies
4581
4.12
1.17
100.00%
66.67%
0.65
Sand
2762
2.48
0.7
100.00%
66.67%
1.00
Fallow land
33664
30.29
8.58
75.00%
100.00%
0.65
Forest
64377
57.93
16.41
85.71%
85.71%
0.84
Grass land
16933
15.24
4.31
80.00%
100.00%
0.76
Agricultural land
223339
201.01
56.91
100.00%
83.33%
0.78
Shrub land
87838
29.48
8.35
83.33%
100.00%
1.00
Overall Classification Accuracy = 88.00%
Overall Kappa Statistics = 0.85
Table 2 Summary statistics of soil organic carbon (SOC, %) content in different soil horizons
Soil Depth
(cm)
N
Mean
Median
Min
Max
SD
CV (%)
Skewness
Kurtosis
0 20
32
0.50
0.58
0.02
0.82
0.32
64.297
0.25
1.30
20 40
32
0.47
0.52
0.05
0.87
0.39
81.79
0.02
1.59
40 100
32
0.43
0.45
0.08
0.99
0.32
75.06
0.11
0.81
(N= Number of samples, Min= Minimum, Max=Maximum, SD= Standard Deviation, CV= Coefficient
of Variation)
Table 3 Comparison of the efficiences and errors of the interpolation methods to predict SOC
Interpolation
Type
Interpolation
method
Soil Depth
(cm)
Efficiency
Error
R2
RMSE
ME
MRE
Deterministic
IDW
0-20
0.776
0.125
0.568
0.214
20-40
0.791
0.121
0.385
0.254
40-100
0.808
0.145
0.645
0.210
LPI
0-20
0.792
0.130
0.398
0.228
20-40
0.816
0.127
0.257
0.251
40-100
0.851
0.148
0.468
0.216
RBF
0-20
0.742
0.176
0.845
0.268
20-40
0.765
0.159
0.681
0.289
40-100
0.781
0.147
0.754
0.275
Geostatistical
OK
0-20
0.918
0.110
0.110
0.158
20-40
0.921
0.120
0.124
0.195
40-100
0.938
0.123
0.121
0.154
EBK
0-20
0.879
0.128
0.351
0.245
20-40
0.848
0.127
0.364
0.235
40-100
0.895
0.131
0.358
0.233
R2 = Coefficient of determination, RMSE=root mean square error, ME=mean error, MRE=mean relative error IDW
inverse distance weighting, LPI local polynomial interpolation, RBF radial basis function, OK ordinary kriging and
EB Empirical Bayes model.
Table 4 Summary of semivariogram parameters of best-fitted theoretical model to predict soil
properties and cross-validation statistics
Soil depth (cm)
Best-fit
model
Nugget
(C0)
Sill
(C0 +C)
Range
(m)
Nugget/
Sill
R2
RSS
ME
RMSE
0-20
Exponential
0.15
1.10
1.076
0.14
0.918
0.005
0.110
0.110
20-40
Exponential
0.001
0.97
1.33
0.10
0.921
0.008
0.124
0.120
40-100
Exponential
0.001
1.08
1.21
9.26
0.938
0.003
0.121
0.123
R2 = coefficient of determination, RSS= residual sum square, ME= mean error, RMSE = root
mean square error
Table 5 Summary of the performance of interpolation methods in terms of improvement over
radial basis finction method
Performance
Soil depth
(cm)
Reduction in RMSE over
RBF (%)
Reduction in MRE over RBF (%)
Increase in R2 over RBF (%)
IDW
LPI
OK
EBK
IDW
LPI
OK
EBK
IDW
LPI
OK
EBK
0-20
28.98
26.14
37.5
27.28
20.14
14.93
41.05
8.58
4.58
3.74
23.72
18.46
20-40
23.9
20.13
24.53
20.13
12.11
13.15
32.53
18.69
3.40
6.67
20.39
10.85
40-100
1.37
0.69
16.33
10.89
23.64
21.45
44.00
15.27
3.46
8.96
20.10
14.60
Average
18.08
15.65
26.12
19.43
18.63
16.51
39.19
14.18
3.81
6.45
21.40
14.63
R2 = Coefficient of determination, RMSE=root mean square error, ME=mean error, MRE=mean relative error IDW
inverse distance weighting, LPI local polynomial interpolation, RBF radial basis function, OK ordinary kriging and
EB Empirical Bayes model.
