Bartholomeus, H.

Mulder, V.L.

English

Wageningen Yield 

  
THE INFLUENCE OF SLOPE IN THE QUANTIFICATION OF SOIL IRON 
CONTENT WITH SPECTRAL REFLECTANCE BASED IRON INDICES 
 
V.L. Mulder1and H.M. Bartholomeus1 
 
1Laboratory of Geo-Information Science and Remote Sensing, Wageningen University, 
Droevendaalsesteeg 3, P.O. Box 47, 6700 AA Wageningen, The Netherlands -  
titia.mulder@wur.nl, harm.bartholomeus@wur.nl 
 
 
KEYWORDS: Imaging Spectroscopy, Soil iron quantification, influence of slope 
 
 
ABSTRACT:  
 
Remote sensing has proven to be a useful tool to determine the presence of iron over large areas. 
However, in airborne imaging spectroscopy terrain characteristics influence the reflectance. With 
the PARGE/ATCOR model the bias of these characteristics is corrected, but the model does not 
correct for soil BRDF, which leads to different deviations for individual wavelengths. In this 
research the influence of slope on the prediction of soil iron content using spectral reflectance based 
iron indices is assessed. An experimental set-up is designed where the slope of the sample is varied, 
resulting in different illumination angles. From these reflectance data different iron indices are 
calculated; the ratio-based Redness Index and the area and standard deviation after continuum-
removal for the iron absorption features located at 550 nm and 880nm. Linear regression and 
multiple linear regression are used to estimate the soil iron content. Moderately accurate models 
(0.62<R2<0.69) are found with linear regression between iron and the calculated indices, but the R2 
is significantly higher when texture is included in the multiple linear regression analysis 
(0.76<R2<0.82).  From the analysis, it became clear that the ratio based Redness Index is not 
significantly influenced by slope. Slope has minor influence on the area and standard deviation of 
the continuum-removed spectrum at 550 nm. For both the area and the standard deviation of the 
continuum-removed spectrum at 880 nm, slope is clearly influencing the indices. The errors are 
significant, but can be corrected with a correction model.  
 
 
1. INTRODUCTION 
 
Iron is an important indicator in the soil 
science; it is an indicator for soil fertility, soil 
usability and it can indicate the age of the 
deposits [1]. Iron species are also an indicator 
that soil is being formed because iron is 
strongly correlated with the soil weathering 
process on the short and long term [2]. 
Determining the spatial distribution of 
different types of iron with traditional 
fieldwork and laboratory analyses is time-
consuming and expensive. Remote sensing 
has proven to be a useful tool to determine the 
presence of iron in extended areas and various 
research fields [1]. Chemical and physical 
properties of the surface influence the soil 
reflectance and interfere with the iron 
absorption features [2, 3]. Much research has 
been done in the discrimination of soils based 
on a combination of different soil properties 
retrieved from spectral data [4-6]. The main 
reason that the influence of slope on soil 
reflectance is not taken into account is 
because of the assumption that in the 
processing stage the reflectance is corrected 
for this. This is partly true, the 
PARGE/ATCOR model corrects for the bias 
of some terrain characteristics. However, the 
model does not correct for soil BRDF which 
leads to different deviations for individual  
wavelenghts. 
  
 
2. METHODOLOGY 
 
Almost all soil reflectance spectra show a 
steep decrease in reflectance towards the blue 
and ultraviolet wavelengths which is due to a 
strong iron-oxygen charge transfer band that 
extends into the ultraviolet. Other absorption 
bands often occur near 700 nm and 880 nm 
due to the electronic transition of ferric iron. 
Electronic transitions involving ferrous iron 
can cause strong absorption bands near 880 
nm as well. Several weaker absorption bands 
between 400 nm and 550 nm are present due 
to one or the other iron ion. 
 
Continuously reflectance spectra are acquired 
in the laboratory experiment, using an ASD 
fieldspec ProFR spectrometer [7]. An 
experimental set-up is designed where the 
slope of the sample can be varied, resulting in 
different illumination angles. Measurements 
are taken every 50 ranging from a 250 slope 
facing towards the light source to a 250 slope 
facing off the light source. The soil samples 
are taken form the slopes of El Hacho de 
Álora in Southern Spain and analyzed for 
total iron content in the laboratory. Soil 
texture is determined manually by an expert 
according to the FAO classification system 
[8]. The iron extraction method, the 
geological and topographical settings are 
more extensively described in [1].   
 
From the reflectance data three different iron 
indices are calculated; the ratio based Redness 
Index and the area and standard deviation 
after continuum-removal for the iron 
absorption features located at 550 nm and 
880nm. With multiple linear regression and 
general statistics the relation between slope 
and the prediction of soil iron content is 
quantified. Soil texture was manually 
classified and has been implemented as 
second regression parameter. In this article, 
the absorption features are being referred to 
as; D550 for the dip occurring between 400 
and 550, D700 for the dip around 700nm and 
the dip around 880nm is referred to as D880. 
The indices derived from the continuum-
removed spectrum are referred to as D880area 
and D880S.D.. 
 
2.1 Ratio Based Redness Index 
 
 
Weathering products of iron bearing minerals 
contain iron oxides, which will color the soil 
red when these become available to the soil 
[3]. Therefore, the ratio based Redness Index 
can be used as an indicator for soil iron. The 
Redness Index is expressed as the reflectance 
in the red part of the spectrum divided by the 
sum of visible red, green and blue 
reflectances (Eq. 1): 
 
 
R = BRFr / (BRFr +BRFg + BRFb)          (1) 
 
Where  BRFn = the bidirectional reflectance in 
the corresponding part of the visible 
spectrum  
 
BRFn is calculated by (Eq. 2): 
 
 
BRFn= Rt / Rc                  (2) 
 
 
Where  BRFn = the bidirectional reflectance in 
waveband n 
Rt = the radiance from the target 
surface 
Rc = the radiance from the reference 
panel [9] 
 
 
 
 
 
 
 
 
  
2.2 Continuum removal 
 
The normalization of the absorption features 
is based on the convex hull method, which is 
commonly used for normalization of soil  
 
 
reflectance data. For example [10] and [11] 
used the convex hull method successfully for 
the retrieval of soil properties. The 
mathematical theories behind the convex hull 
method are described by [12, 13]. After 
continuum removal, the area of the dip is 
calculated as indicator for iron. The depth and 
width of the absorption dips are represented 
with the standard deviation after continuum 
removal; the larger the width and depth of an 
absorption feature, the higher the standard 
deviation. 
 
2.3 Prediction of the soil iron content. 
 
For the calculation of the iron content, a linear 
regression model was established based on 
the samples measured from nadir (Feest_0). 
The calculated index is used as independent 
variable and iron content measured in the 
laboratory is the dependent variable [1], see 
Eq. 3. 
 
 
Feest_0 = a + b* Index           (3) 
 
 
Next, it is being examined if a multiple linear 
regression will improve the results. Since 
texture is also explaining deviations in 
reflectance, this variable is included as second 
regression parameter (Eq. 4). 
 
 
Feest_0 = a + b * Index + c* Texture           (4) 
 
In order to find out what the influence of 
slope is on the determination of the iron 
content, the soil iron content for sloping 
samples is predicted with the functions 
derived from a nadir position (Fepred_slope(x)). 
The regression functions are applied on the 
index values for different slopes on both the 
calibration and the validation set. Next, the 
difference between the predicted iron from 
nadir and the predicted iron with a slope is 
calculated. The difference is calculated in 
percentages so results are normalized and a 
comparison can be made between different 
iron contents. The significance of this error is 
determined by means of a Paired-Samples T-
test. When the 2-tailed significance is smaller 
than 0.05 slope has a significant influence on 
the determination of the iron content [14].  
 
Finally, a slope correction model is 
developed. The regression function, based on 
the calibration data set, must predict the 
correction for each index and slope, with the 
estimated error as dependent variable.  The 
performance of the slope correction models is 
assessed with the standard error of calibration 
(SEC), standard error of prediction (SEP), the 
bias and the ratio of performance to deviation 
(RPD) values [15, 16]. 
 
 
 3. RESULTS AND DISCUSSION 
 
The reflectance of bare soil varies with the 
slope (Fig. 1). Up to 600 nm the differences 
are small. At higher wavelengths the 
deviation in reflectance from nadir increases. 
Around 1000 nm differences in reflectance 
for a negative slope deviate up to -6% and for 
positive slopes up to 2%. The maximum 
difference can be found around 1800 nm, with 
a difference up to -8% for the negative facing 
slopes and up to 3% for the positive slopes. 
The specific absorption features from iron are 
clearly visible, from 390 to 600 nm, around 
700 nm, and from 800 nm up to 1000 nm. It 
can be concluded that the deviation from 
nadir is larger for the slopes facing off the 
light source than for the slopes facing towards 
the light source.  
 
  
 
Figure 1: Reflectance of bare soil under different slopes. 
 
In Table 2 the overall correlation (R) between 
the iron indices and the iron content of the 
soil samples measured in the laboratory are 
given. The ratio based Redness Index has an 
average correlation of 0.80. D550area has an 
average correlation of -0.82 and D550S.D. has 
a correlation of 0.82, which means that with 
decreasing iron content the area of the dip 
decreases as well. For D700 the average 
correlations are much lower: -0.53 for 
D700S.D.  and 0.51 for D700area. The 
correlation for D880area is on average -0.84 
and 0.84 for D880S.D.. The correlation of 
D700 is almost as low as a random relation. 
Therefore, this absorption feature will not be 
used for the next part of the research. 
 
The R2 for linear regression is significantly 
lower compared to multiple linear regression. 
For linear regression, the results vary between 
0.62 up to 0.69 for the calibration set and 
between 0.68 up to 0.77 for the validation set. 
Higher R2 values are found for multiple linear 
regression when soil texture is included. 
Values range from 0.76 up to 0.82 for the 
calibration set and from 0.77 up to 0.82 for 
the calibration set. It can be concluded that 
the multiple regression functions have a better 
performance and that texture does improve 
the prediction of soil iron content, so these 
functions will be used to estimate soil iron 
content. The significance of the effect of 
slope on the estimation of soil iron content is 
tested by means of paired-samples T-Test. 
The pairs that are compared are the prediction 
values of iron content under a certain slope 
with the estimation values of iron content 
measured at nadir. Values have been tested on 
the 95% confidence interval for the error in 
iron content in mg/kg. If the 2-tailed 
significance is lower than 0.05 the deviation 
of iron content is significant. The results are 
given in Table 3 where the significant 
deviations are given in red. 
 
Table 2: Average correlation coefficient (R) of iron and spectral reflectance based iron indices 
under different slopes. 
RI D550Area D550S.D. D700Area D700S.D. D880Area D880S.D.
Mean 0.798 -0.817 0.817 0.512 -0.534 -0.835 0.839
S.D. 0.002 0.005 0.004 0.067 0.058 0.005 0.002
 
 
 
 
 
 
 
  
Table 3: 2-tailed significance of the compared pairs, the significant differences are given in italic. 
Slope (°) RI D550Area D550S.D. D880Area D880S.D. 
-25 0.061 0.027 3.22E-11 1.81E-07 6.51E-19 
-20 0.236 0.003 2.27E-08 4.74E-09 1.08E-21 
-15 0.956 0.016 5.24E-09 2.56E-07 6.02E-21 
-10 0.053 0.12 2.06E-07 7.40E-08 6.38E-21 
-5 0.011 0.177 3.79E-07 1.07E-09 3.82E-24 
5 0.467 0.022 0.139091 0.433653 1.26E-05 
10 0.525 0.421 0.00029 0.043252 2.57E-10 
15 0.644 0.03 2.22E-06 0.007264 6.23E-11 
20 0.872 0 2.84E-06 0.000204 3.34E-14 
25 0.791 0.001 5.72E-06 8.07E-05 1.25E-19 
 
The differences between the estimated iron 
content at nadir and the predicted iron content 
under a certain slope do not significantly 
differ for the Redness Index except for a slope 
of -50 (facing off the light source). The 
differences for D550area are partly significant. 
For slopes larger than +150 and -150 the 
deviation is significant, for smaller slopes the 
model is robust, except for +50. These results 
show that slope has significant influence on 
the iron prediction. For both the area and the 
S.D. of D880 all values are smaller than 0.05 
except for D880 with +50. From this test it 
can be concluded that the Redness Index is 
robust and performing well under varying 
slopes. The continuum removed indices 
appear to be very sensitive to variations in 
slope. The differences are higher for the 
negative facing slopes; this might be due to 
the retroreflectance properties of the material 
[2] and the non-lambertian behavior of the 
surface [14]. One reason that D880 performs 
better is that this adsorption dip is caused by 
only the mineralogical composition. The 
major bearing iron mineral is hematite which 
will give an adsorption dip around 900 nm 
and is directly related to texture while other 
features are not influencing the dip as is the 
case in the VIR. Since texture is only included 
as extra variable in the prediction model, 
D880 performs best. 
 
 
 
 
A slope correction model is developed for all 
indices but in this paper only the results are 
shown for D880S.D. because the errors are the 
largest for this index. The mean error has 
become 0 after the application of the slope 
correction model and the V-shape is no longer 
present (Fig. 4a). The performance of the 
model when applied on the validation set is 
good because the slopes do not deviate 
anymore and the model has corrected for the 
so called ‘V-shape’ (Fig. 4b). 
 
The SEC values range between 1.09 and 1.15 
mg/kg and the SEP values varies between 
1.87 and 1.94 mg/kg. The bias values ranges 
between -1.78 and -1.86 mg/kg. The bias is 
negative which means that iron content is 
being underestimated when the terrain is 
sloping. The bias is relative small and the R2 
values are 0.76 and 0.77 which is good. The 
RPD values are all larger than 2, which means 
that this model can be classified as a class A 
model according to [15]. The correction 
model would be better if after the correction 
the standard deviation would become smaller. 
This is not the case because the regression 
function only corrects for the bias of the 
estimation. The standard deviation can only 
decrease if the uncorrected data can be 
aggregated by a third soil attribute.  
 
 
 
 
 
 
  
Figure 4a: Mean error of the predicted iron 
content for corrected and uncorrected data of 
the calibration set for D880S.D. 
Figure 4b: Mean error of the predicted iron 
content for corrected and uncorrected data of 
the validation set for D880S.D. 
 
4. CONCLUSIONS 
 
Linear regression and multiple linear 
regression have been used to estimate the soil 
iron content using spectral indices. The R2 is 
significantly higher when multiple linear 
regression with both index and texture is used 
for the estimation of soil iron content. It 
became clear that the Redness Index is not 
significantly influenced by slope. Slope has 
minor influence if iron is estimated using the 
area and standard deviation of the continuum-
removed spectrum at 550 nm. The error 
increases with increasing slope but there is no 
clear trend visible. 
For both the area and the standard deviation 
of the continuum-removed spectrum at 880 
nm the slope is clearly influencing the indices 
and errors are significantly. The effect is 
stronger for the slopes facing away from the 
light source, which might be due to the 
retroreflectance properties of the material and 
the surface roughness. A correction model, 
which uses slope and wavelength as input 
variables, is developed to minimize the 
estimation error caused by slope and was able 
to correct the disturbing effect of slope well. 
 
 
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The influence of slope in the quantification of soil iron content with spectral reflectance based iron indices

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The influence of slope in the quantification of soil iron content with spectral reflectance based iron indices

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