NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

Contract No. DE-AC36-08GO28308

Multivariate Calibration Models 

for Sorghum Composition using 

Near-Infrared Spectroscopy 

E. Wolfrum and C. Payne

National Renewable Energy Laboratory

T. Stefaniak and W. Rooney

Texas A&M University

N. Dighe

Monsanto

B. Bean

Texas Agrilife Research and Extension

J. Dahlberg

Kearney Research and Extension Center

Technical Report

NREL/TP-5100-56838

March 2013
NREL is a national laboratory of the U.S. Department of Energy, Office of Energy 

Efficiency & Renewable Energy, operated by the Alliance for Sustainable Energy, LLC.

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, Colorado 80401

303-275-3000 • www.nrel.gov

Contract No. DE-AC36-08GO28308

Multivariate Calibration Models 

for Sorghum Composition 

using Near-Infrared 

Spectroscopy 

E. Wolfrum and C. Payne

National Renewable Energy Laboratory

T. Stefaniak and W. Rooney

Texas A&M University

N. Dighe

Monsanto/Texas A&M University

B. Bean

Texas Agrilife Research and Extension

J. Dahlberg

Kearney Research and Extension Center

Prepared under Task No. BB07.2510

Technical Report

NREL/TP-5100-56838

March 2013
NOTICE

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iii

Abstract

We have developed calibration models based on near-infrared (NIR) spectroscopy coupled with 

multivariate statistics to predict compositional properties relevant to cellulosic biofuels 

production for a variety of sorghum cultivars. A robust calibration population was developed in 

an iterative fashion. The quality of models developed using the same sample geometry on two 

different types of NIR spectrometers and two different sample geometries on the same 

spectrometer did not vary greatly. 
iv

List of Acronyms

FT-NIR Fourier transform near-infrared

HPLC high performance liquid chromatography 

NIR near-infrared

PC principal component 

PLS partial least squares

RMSECV root mean standard error of cross-validation 

sd standard deviation 

SNV standard normal variate

UV/VIS ultraviolet-visible spectroscopy
v 

Table of Contents

1 Introduction........................................................................................................................................... 1

2 Materials and Methods......................................................................................................................... 1

2.1 Sample Selection.............................................................................................................................. 1

2.2 Biomass Analysis............................................................................................................................. 1

2.3 Near-Infrared Spectroscopy ............................................................................................................. 1

2.4 Multivariate Analysis....................................................................................................................... 2

3 Results and Discussion....................................................................................................................... 2

3.1 Sample Selection.............................................................................................................................. 2

3.2 Calibration Model Results ............................................................................................................... 3

4 Conclusions .......................................................................................................................................... 6

References................................................................................................................................................... 7
1 

1 Introduction

There is great interest in the development of sustainable biofuels to displace petroleum and other 

fossil fuels, and investigations into a variety of dedicated bioenergy feedstocks are underway [1-

6]. Sorghum [Sorghum bicolor (L.) Moench] is one such dedicated bioenergy feedstock. Recent 

publications discuss the compositional variety and agronomic traits of different sorghum 

cultivars [7-12]. Rapid compositional analysis methods based on near-infrared (NIR) reflectance 

spectroscopy combined with multivariate statistics are well-established and widely used in 

agriculture [13-15]. Rapid compositional analysis methods have been developed for a number of 

different potential bioenergy feedstocks [16-18]. The goal of this work was to develop an NIR 

calibration model for sorghum as a rapid analysis tool for sorghum researchers. 

2 Materials and Methods

2.1 Sample Selection

Sorghum samples were taken from various breeding and agronomic trials conducted by the 

Texas Agrilife Research Sorghum Breeding program. The samples were collected from tests 

located in several different locations in Texas and a detailed description of the samples and their 

compositional variety has recently been published [9, 10]. Once all the samples were collected, 

they were dried in a forced air drier at 45°C. Samples were then knife-milled to pass through a 2-

mm screen and stored at ambient temperature in paper bags.

2.2 Biomass Analysis 

Samples were analyzed using standard methods for summative biomass compositional analysis. 

A detailed review of the history of these methods and typical analytical uncertainties are 

available [19, 20]. Mass closures were close to 100%, with no systematic variation by sorghum 

type. A detailed discussion of the results of these analyses is presented elsewhere [9, 10]. The 

samples were analyzed in groups of five to eight over the course of several months. Table 1 

shows the summary compositional analysis results for the sorghum samples.

One modification to the standard analytical methods described above was the determination of 

starch in the samples. We performed starch analysis on all samples as received using a standard 

assay procedure with HPLC rather than UV/VIS detection of the resulting glucose (Megazyme). 

We refer to this as-received value as the whole starch content. Any sample containing more than 

2% whole starch was also analyzed after water/ethanol extraction to determine the remaining 

amount of structural starch. This was necessary because the analytical hydrolysis procedure 

described above, used to break down cellulose to glucose, will also hydrolyze any structural 

starch that is present to glucose. In the absence of starch, all glucose is reported as structural 

glucan. With starch present, the structural glucan value must be corrected for structural starch.

Of the 155 samples, 113 had non-zero amounts of whole starch, and 64 had non-zero amounts of 

structural starch.

2.3 Near-Infrared Spectroscopy

Two types of NIR spectrometers were used in this work: a grating-monochrometer type (XDS, 

Foss North America, Eden Prairie, MN) and a Fourier transform (FT) type (Antaris, Thermo-
2 

Fisher, Waltham, MA). The spectral range for the grating-monochrometer unit (hereafter referred 

to as the NIR unit) was 400–2,500 nm, although only the region of 1,100–2,500 nm was used for 

calibration model development. The spectral range of the Fourier transform unit (hereafter 

referred to as the FT-NIR unit) was 3,700–12,000 cm

-1, although only the region of 4,000–9,000 

cm

-1 was used for calibration model development. The spectral regions of the two instruments 

used for modeling are quite similar, and conversion between wavelength and wavenumber is 

straightforward (cm-1=107

/nm).

Knife-milled samples were placed in quartz sample cups and scanned in reflectance mode on 

both the NIR and FT-NIR instruments. Samples were also scanned in reflectance mode on the 

FT-NIR instrument using an automated sampling carousel and borosilicate sampling vials 

(Thermo-Fisher p/n 03-339-26C). All samples were scanned in either duplicate or triplicate. 

Replicate scans were averaged prior to building calibration models. Quality-control (“check”) 

materials were scanned along with the experimental samples to ensure instrument stability; no 

anomalies were seen with the check scans.

2.4 Multivariate Analysis 

Multivariate analyses were performed in Unscrambler 10.1 (Camo Inc., www.camo.com). Some 

data manipulation and statistical analyses were performed in R (R Project for Statistical 

Computing, www.r-project.org). The quality of a calibration model was assessed (and different 

calibration models were compared) based on the correlation coefficient R and the root mean 

standard error of cross-validation (RMSECV). Correlation coefficients were first converted to zvalues using the Fisher z-transform, and then differences were compared using a pooled standard 

error 1/( 1)3 /( )3 σ n1 n2 −+−= to the critical z-value of 1.96. Because the RMSECV values are 

the square root of a variance measure (in this case the variance of predicted and calibration 

values), the ratios of the squares of these values are compared to a critical F-value. 

Two types of partial least squares (PLS) calibration models were developed: grouped PLS-1 and 

PLS-2. The critical difference between the two types is that the grouped PLS-1 algorithm creates 

a calibration equation for each variable (in this case, for each constituent in sorghum) separately. 

The PLS-2 algorithm creates single calibration equations for the variable set at once; all 

constituent models are solved simultaneously. 

3 Results and Discussion

3.1 Sample Selection

Multivariate calibration models are secondary analytical techniques in that they require primary 

analytical data for calibration. Thus, a robust multivariate calibration model requires a sufficient 

number of representative samples with primary analytical data. Sample selection for the 

calibration models discussed here proceeded in an iterative manner. The first group of sorghum 

samples analyzed and included in the model included only commercially-available cultivars. 

Preliminary calibration models were developed using these samples and were used to predict 

later populations that included more experimental germplasm. Samples from these later 

populations were selected for wet chemical analysis for a number of reasons: they represented 

unique agronomic properties, they were poorly predicted by the preliminary model, or they had 
3 

NIR spectra that were distinct from the original model population. Table 1 shows the summary 

statistics for the compositional analysis of the 155 sorghum samples used in this work. 

3.2 Calibration Model Results

The average spectrum of the entire calibration set collected using each instrument assembly is 

shown in Figure 1. Table 2 shows the summary calibration statistics for PLS-2 models developed 

for each instrument assembly for the constituent glucan. We found that calibration models 

improved when the active wavelength ranges of the spectra were truncated to 4,000–9,000 cm-1

for the FT-NIR system and 1,100–2,500 nm for the NIR system. These are essentially the same 

ranges because 4,000–9,000 cm-1 is equivalent to 1,111–2,500 nm. Using derivatization and 

smoothing improved the models as well; we saw a broad maximum in model quality with respect 

to the size of the window for Savitsky-Golay derivative smoothing. The 21-point window was 

used to produce the models discussed here; this value was a compromise that provided smooth 

regression coefficients for each constituent as well as optimal RMSECV values. Although the 

RMSECV value for the NIR assembly is slightly higher than for the FT-NIR assemblies, 

statistical analysis of the data in Table 2 showed no differences in RMSECV or R2

 values for any 

of the models; the cross validation results suggest that all models are equivalent.

Figure 1. Average spectra taken with each spectrometer assembly (NIR sample cup, FT-NIR 

sample cup, FT-NIR autosampler). The NIR spectra abscissa for the diffraction-based instrument 

(NIR sample cup) was converted from wavelength to wavenumber for the plots
4 

Table 1. Summary Statistics for the 155 Sorghum Samples Used to Develop Calibration Models 

All constituent values are in dry weight percent. The samples were taken from a variety of agronomic field 

trials conducted at Texas Agrilife Research Stations.

Constituent Mean Max Min SD

Glucan 27.8 38.2 17.6 5.7

Xylan 16.0 21.2 10.8 2.6

Lignin 13.2 20.6 8.9 2.9

Starch 9.0 30.9 0.0 8.0

Extractives 27.2 49.9 13.3 8.7

Ash 6.8 11.3 2.3 2.0

Table 2. Summary Statistics for PLS-2 Calibration Models for Glucan Content in Sorghum Using 

Three Different Sets of NIR Spectra 

Spectral ranges are expressed in wavenumbers (cm-1) for the FT-NIR instrument and in wavelength (nm) 

for the diffraction NIR unit; the spectral ranges are essentially equivalent. The “Combined FT-NIR” model 

used both the sample cup and the autosampler spectra.

Instrument/Model Spectral Range RMSECV R2 PCs (#) Samples (#)

NIR Sample Cup 1,100–2,500 1.48 0.93 7 130

FT-NIR Sample Cup 4,000–9,000 1.24 0.95 6 134

FT-NIR Autosampler 4,000–9,000 1.25 0.95 5 121

Combined FT-NIR 4,000–9,000 1.52 0.93 7 261

Table 3. Summary Statistics for PLS-2 and PLS-1 Calibration Models for the Major Constituents 

(Glucan, Xylan, Lignin, Starch, Total Extractives, and Ash) of Sorghum Using FT-NIR Sample Cup 

Spectra 

Spectra underwent pretreatment prior to model-building. The PLS-2 model used six principal components 

(PCs) and had 134 samples. We saw no significant differences between PLS-1 and PLS-2 model 

statistics (p=0.05). Reference method uncertainty values are expressed as twice the standard deviation 

(sd) of replicate measurements and are taken from [20] except for starch, which is estimated as twice the 

sd of replicate measurement (unpublished results).

PLS-2 Model PLS-1 Model Reference Method 

Uncertainty Constituent RMSECV R2 RMSECV R2 PCs (#) Samples (#)

Glucan 1.24 0.95 1.45 0.94 5 147 1.0

Xylan 0.85 0.89 0.81 0.90 4 147 0.6

Lignin 0.86 0.91 0.82 0.92 3 151 0.4

Starch 2.33 0.91 2.43 0.90 5 140 0.6

Extractives 2.29 0.91 2.33 0.93 5 146 1.2

Ash 0.88 0.81 0.78 0.85 6 148 0.4
5 

Summary statistics for the grouped PLS-1 and PLS-2 models for the FT-NIR sample cup spectra 

are shown in Table 3 along with the uncertainties of the primary analytical methods [20], and 

plots of the predicted vs. measured constituent values for the constituents in the PLS-2 

calibration model are shown in Figure 2. There are no significant differences between the 

grouped PLS-1 and the PLS-2 models; both algorithms provide equivalent results. The PLS-1 

models require fewer principal components, but a separate model is required for each 

constituent. 

Figure 2. Predicted vs. measured composition for FT-NIR quartz cell calibration model: (a) glucan, 

(b) xylan, (c) lignin, (d) starch, (e) extractives, (f) ash. Some constituent predictions exhibit greater 

uncertainty than others.

(a) (b)

(c) (d)

(e) (f)
6 

As the data in Table 2 indicate, there is little difference between the calibration models using FTNIR sample cup spectra and FT-NIR autosampler vial spectra. Each model could predict samples 

from the other model successfully, although there was approximately a two-fold higher 

uncertainty associated with the predictions (data not shown). A calibration model combining 

both the sample cup and autosampler vial spectra showed results similar to the individual 

models, although the RMSECV value is higher (p=0.05). These results suggest that with proper 

spectral pretreatment, a hybrid model consisting of samples taken with different sampling 

geometries may be possible. This is useful for two reasons. First, the borosilicate autosampler is

a commodity item, available in large quantity very inexpensively. Second, samples can be stored 

in the autosampler vials immediately after milling, so the spectra of a given sample can be 

collected without additional handling of the sample. This minimizes operator effort and also 

reduces the opportunity for sample spillage or loss.

4 Conclusions

Robust multivariate calibration models using NIR spectroscopy coupled with chemometrics can 

be used as a rapid analysis tool for determining sorghum composition relevant for biofuels 

production. Sample selection is critical to building a robust model; multivariate calibration 

models must contain samples similar to those to be predicted. Standard spectral pretreatment 

methods reduce the number of principal components required for a model. Models developed on 

different types of NIR spectrometers, and with different sampling geometries, provided 

essentially equivalent results. 

We intend to continue development of the calibration models presented here. Integration of new 

samples (particularly those with interesting agronomic or genetic traits) as well as samples 

poorly predicted by the current models will increase the robustness of the model. With proper 

laboratory quality control processes in place to ensure the stability of instrument response over 

time, new samples can routinely be added as they are identified and undergo wet chemical 

analysis.
7 

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