Soil radiance spectra (passive mode emission measurements) in the TIR were recorded at Commonwealth Scientific and Industrial Research Organisation (CSIRO) laboratories (Perth, Western Australia) using a micro Fourier Transform Interferometer (μFTIR) (model 102, Design&Prototypes instruments, http://www.dpinstruments.com) with a spectral resolution of 6 cm⁻¹ via a fore optic with a 4.5° field of view from ∼250 mm height, resulting in an GFOV of ∼20 mm. The instrument was equipped with a liquid-nitrogen-cooled two element detector (dual InSb/MCT) and measured radiance within the spectral range from 2 to 16 μm. However the range used in this study was limited to the wavelength within the atmospheric window from 7 to 14 μm, restricted by the range of the MCT detector.

Each soil sample measurement was composed of four individual spectral radiance readings: (1) warm blackbody; (2) cold blackbody; (3) downwelling radiance; and (4) soil surface radiance. Calibration and emissivity calculation followed the methods of [22–24].

(1) and (2):

The μFTIR was radiometrically calibrated using a blackbody (model 41P, D&P instruments) attached to the fore optics, adjusted for two different temperatures. For the first reading it was set just above the sample temperature (T_warm: 65 °C) and for the second one just below the ambient temperature (T_cold: 25 °C). The temperature settings were held within this region to minimize potential nonlinearities from the instrument [25].

A linear relationship between the instrument’s DN values and the observed at sensor radiance was assumed (L(λ) = α(λ) × DN(λ) + β(λ)), so that both wavelength dependent instrumental factors, gains (α(λ)) and offsets (β(λ)), could be calculated from the two blackbody measurements. Gains, which represent the instrument’s spectral response, were calculated from Equation (1): (1) α ( λ ) = DN warm ( λ ) − DN cold ( λ ) B ( T warm ,   λ ) − B ( T cold ,   λ )where B(T, λ) is the spectral radiance, for each of the calibration blackbodies, retrieved from Planck’s blackbody function.

Offsets, incorporating electrical factors and the instrument’s self-emission, could be retrieved from either blackbody by Equation (2): (2) β ( λ ) = DN ( λ ) − L ( λ ) × B ( T ,   λ )

(3) and (4):

During the measurement with the μFTIR the background downwelling radiance, which is emitted from the ceiling, the walls and the atmosphere (in particular above the sample) in the laboratory, is reflected from the surface of the sample and recorded by the instrument on top of the sample radiance measurement. Downwelling radiance was measured via a diffuse reflective brass plate just before the soil sample reading.

The brass plate is spectrally flat and has a emissivity of ε∼0.25. Following Kirchhoff’s law (ε = 1 – R) [26], the complementary reflectance is R∼0.75, and accordingly can be assumed that the at sensor radiance recorded by the instrument, when the brass plate is measured, is a good estimate for the downwelling radiance (L_DW (λ)), which was calculated from Equation (3): (3) L DW   ( λ ) = L BP   ( λ ) − ε BP   ( λ ) B ( T BP ,   λ ) 1 − ε BP   ( λ )where L_BP (λ) is the spectral radiance, and ε_BP (λ) the emissivity of the brass plate. B(T_BP, λ) is the Planck blackbody spectral radiance of the brass plate at its temperature T_BP. Note, that for these measurements, highly defuse gold plates (ε∼0.03–0.06) are also common. L_DW (λ) measured off the brass plate will be more accurately calibrated to radiance units than off a gold plate when outdoor measurements are done under extreme cold background temperature conditions [27]. For laboratory measurements, however, where the plate’s temperature is close to the ambient temperature, the absolute emissivity/reflectance of the plate is not an issue anymore, as long as the background temperature is estimated well enough. The background temperature was measured by a thermocouple thermometer physically attached to the back of the brass plate and provided ±0.1 °C accuracy.

Finally, the sample surface was measured, which was preheated (60 °C) before in an oven. The measurement of relatively hot samples above the background room temperature ensured an improved signal to noise ratio (SNR). The instruments integration time (16 scan cycles) was adjusted to keep its temperature decrease to a minimum during recording time. Having calculated the soil surface radiance (L_S(λ)), its emissivity (ε_S(λ)), corrected for downwelling radiance, could be derived by Equation (4). (4) ε S   ( λ ) = L S   ( λ ) − L DW   ( λ ) B ( T S ,   λ ) − L DW   ( λ )

However, solving Equation (4) requires the soil surface temperature to be known (which is especially difficult for remote sensing data). For that purpose an inverse Planck curve fitting algorithm was applied to estimate the temperature. Assuming that for a specific wavelength range the emissivity is constant and known, identical temperatures for these wavelengths could be derived by using the inverse Planck function as a function of radiance. For the soils in the Mullewa region, which are dominated by silicate minerals, this assumption is true, where typically the silicate Christiansen frequency features occur. In this region the emissivity values are at their highest (close to ε = 1, see Figure 1), and thus the highest apparent radiant temperatures of the sample. Considering increasing instrument noise at shorter wavelength the range between 7.7 and 7.8 μm was selected for the temperature emissivity separation algorithm. Within this range the algorithm identified the maximum emissivity, approaching 1.0. Software developed by Andy Green (pers. comm.) of CSIRO was used to apply the above processing steps.

Note that the path atmospheric spectra transmissivity between the target and the instrument has not been considered in the above equations, as it becomes negligible for short distances, as has been used in our setup [23]. Bands between 7 and 7.63 μm were excluded from the spectral range in further analyses due to extreme noise levels, resulting in 208 spectral bands.

Soil surface bidirectional reflectance in the VNIR-SWIR spectral region was measured in the laboratory on the samples using an Analytical Spectral Devices (ASD) Inc FieldSpec-Pro (http://www.asdi.com) spectrometer with a contact probe (GFOV∼10 mm). The Spectral resolution is 3–4 nm in the 0.35- to 1.0-μm region (spectral sampling 1.4 nm), and 10–12 nm in the 1.0- to 2.5-μm region (spectral sampling 2 nm). The entire spectrum is resampled at 1 nm for display purposes, which resulted in 2,151 spectral bands. The measurements were performed straight after the TIR measurements, without any interference to ensure that the soil surfaces were similar as possible for both TIR and VNIR-SWIR measurements. The ASD spectra were subsequently corrected to absolute reflectance using the white reference measurement of a spectralon panel (http://www.labsphere.com/) taken before soil radiance measurements.

The spectra were resampled to operational imagery sensor spectral specifications for both wavelength regions, the VNIR-SWIR and the thermal infrared range. ASD spectra were resampled to HyMap spectral characteristics (2010 HyVISTA Co., http://www.hyvista.com), with 125 bands and a full width half maximum (FWHM) between 15–20 nm, covering the spectral range from 450- to 2,480-nm. The TIR spectra were resampled to TASI-600 specifications (2009 ITRES Research Limited), which possess 32 bands with a FWHM of 125 nm and a spectral range from 8 to 11.4 μm. Figure 1 shows the defined sensors’ spectral response functions (SRF), which follows their defined spectral characteristics.

HyMAP and TASI-600 were chosen as representative hyperspectral sensors that possessed specifications most suited to the aim of this study. Data from the HyMAP instrument has been used extensively in the past 10–15 years in all areas of the world and is nowadays one of the most used and known airborne hyperspectral imager for the VNIR-SWIR region. The TASI-600 is one of the very few airborne TIR sensors currently available. The spatially enhanced broadband array spectrograph system (SEBASS) covers a broader spectral range from 7.5 to 13.5 μm (128 contiguous spectral bands). We have decided to test the TIR potential by resampling to the TASI-600 sensor characteristics for two reasons. The TASI-600 is more accessible than the SEBASS sensor. We also wanted to see whether the slightly reduced spectral coverage and resolution of TASI-600 is sufficient for the aim of this study.

The TIR spectra were converted to reflectance using Kirchhoff’s law. The resampled TIR and the VNIR-SWIR laboratory soil spectra were transformed from reflectance (R) to absorbance (log₁₀(1/R)), as input to the statistical analyses, to be consistent with the Beer–Lambert law [28].

The 45 samples from the original dataset were divided into a training or calibration dataset of 30 samples, and 15 samples were used as a test dataset for an independent external validation. The extended dataset contains all of the 55 samples, including the extreme clay rich samples, thus did not allow a representative individual test dataset for an independent external validation. For this case, an internal validation method (full cross-validation) was used to assess the prediction accuracy of the PLSR models.

In the calibration, PLSR establishes a multivariate regression model, based on the training or calibration dataset. This involved the reducing of the high dimensional X data to a few factors (latent variables), which concentrate the spectral information that is relevant to predict Y. This essential information is stored within the first factors, while higher factors contain decreasing Y-relevance and increasing noise data.

To assess the models performance with respect to its dimensionality, a full cross validation (leave-one-out validation) was employed. The models were evaluated based on the following properties: lowest number of factors as a measure of model robustness, the lowest root mean square error of prediction (RMSEP) as a measure of expected error in future predictions, and the coefficient of determination (R²).

Predicted versus observed plots are used to display the Y-values, which are predicted from the regression models. The closer the trend line of the calibration stage follows the trend line of the validation stage, the more robust the model can be rated in terms of the samples used for the validation.

The influence of each of the spectral bands in terms of their informative contribution for predicting the soil parameter of interest was assessed by interpreting the pattern of the model’s loading weights and its regression coefficients.

Loading weights (w) describe the relationships between the X- and the Y-variables. High loading weights (in the positive and in the negative dimension) indicate spectral bands being important in this relationship, and hence have a positive or negative link with the predicted soil parameter in that specific factor. Loading weights from different factors can be judged by their proportion of the total explained variance [14]. If the loading weights as a function of wavelength reveal spectral characteristics related to known physical and chemical sample constituents, they can be defined as the spectral driver for the model within that factor.

For the final PLSR model, the regression coefficients are generated, which can be interpreted spectrally in the same way as the loading weights. However, they combine the loading weights information from each of the selected factors. Thus, the regression coefficients reveal the most influential spectral bands of the selected PLSR model for the soil parameter of interest.

All of the three spectral ranges (VNIR-SWIR, TIR, and VNIR-SWIR-TIR) were able to predict the soil’s very small range of clay content (<15%) from the original dataset. The TIR performed best amongst them, as it was able to predict the clay content with a 3 factor model (Figure 6). Applying this model to the test dataset, the clay content could be predicted with a R² of 0.93 and a RMSEP of 0.66%. The combination of the TIR with the VNIR-SWIR spectral range did not improve the TIR performance, since the VNIR-SWIR-TIR model needed 5 factors to predict the clay content with a R² of 0.84 and a RMSEP of 0.98%. Using only the VNIR-SWIR spectral range did result in a slightly better performance than its combination with the TIR (5 factor model with a R² of 0.89 and a RMSEP of 0.81%).

The models for predicting the sand content of the soils in the original dataset revealed good results for the TIR and the VNIR-SWIR-TIR combination (Figure 7). The PLSR analysis was not able to create an adequate model from the VNIR-SWIR wavelength alone. Similar to the clay content, the TIR model on its own performed best, as 3 factors were sufficient to built a stable model, which predicted the sand content with a R² of 0.93 and a RMSEP of 0.82%. The VNIR-SWIR-TIR produced the best results with 5 factor model (R² = 0.9 and RMSEP = 0.97%).

The soil’s content of organic carbon could be predicted from all of the three spectral ranges, despite of the very low content of <1.5%. The TIR, which does not contain diagnostic organic spectral features, produced good results in the cross-validation stage (5 factors, R² of 0.91 and a RMSEP of 0.08%). However, the model resulted in moderate prediction abilities for the test dataset (R² of 0.62 and a RMSEP of 0.12%). The best result was achieved with the combination of the VNIR-SWIR-TIR spectral range (Figure 8). A PLSR model with 5 factors was able to predict the organic carbon content with a R² of 0.95 and a RMSEP of 0.04%.

Figure 9 provides an insight to the drivers (also referred to as “inner relations”) for the VNIR-SWIR-TIR models. The regression coefficients for the combined VNIR-SWIR-TIR models identify the significance of a spectral region for the prediction of the soil parameter of interest. Similar to the interpretation of the loading weights within a specific factor, the correlation coefficients relate to the spectral bands of importance for the final all factor combined PLSR model.

As expected, the variables clay and sand reveal their inverse relationship in their regression coefficient patterns, at least within the most important regions of the TIR and the SWIR. Figure 9 shows that the SWIR and the TIR are the most important spectral regions for the prediction of clay and sand content, which fit with the occurrence of the most distinctive textural spectral features (clay minerals, such as kaolinite and silicates, and quartz) for these wavelengths. In spite of the regression coefficients being composed of the combined information from all of the used loading weights, they still are consistent with the diagnostic spectral features. For example, the kaolinite features at 2.2 μm, at 9.0 μm, at 9.8 μm, and between 10.6–10.8 μm (red arrows). There is a subtle suggestion of the 2.2 μm kaolinite doublet feature too.

Furthermore the first lobe of the quartz Reststrahlen bands starting at 8 μm displays a steep stair-like descent towards longer wavelength (blue arrows), indicating its prominent role as the driver for grain size variations. This effect is likely to be associated with the reduction in spectral contrast of the Reststrahlen bands with decreasing grain size [30,34]. However, it should be noted that more complicated interactions of radiation with mixtures of fine quartz and/or clay particles coating quartz sand grains can also reduce the Reststrahlen spectral contrast [35].

The organic carbon content PLSR model indicates that the TIR wavelengths are valuable input for its prediction. However, the most important spectral bands are found in the VNIR region, which is consistent with the literature, where spectral features in the VIS region are identified as being related to the presence of organic compounds (green arrow). The change in slope in the VIS is a function of the soil organic matter content [6,36], which is represented as increasing regression coefficient values from 588 nm to 710 nm (Figure 9). Subsequently they decrease towards a trough with a minimum at 900 nm, which is associated with features of iron bearing minerals such as haematite (880 nm) and goethite (920 nm). The feature located at around 500 nm is also due to the iron oxide charge transfer feature in the ultraviolet/visible wavelength region [37]. Note, since the soils’ iron oxide content has not been measured to this point of the research, we cannot ascertain if the relationship between soil organic carbon and the reflectance spectra is due to an association with this or any other unmeasured parameter.

The interpretation of the PLSR models’ loading weights for a particular factor reveals a more detailed view of the models drivers relative to the shape of the soils’ spectral features. With the focus on the TIR spectral region, the texture’s inverse relationship of the two response variables sand and clay is clearly evident again. Figure 10 shows the loading weights for the 3 factors (f1, f2, and f3), involved with both models. The loading weights for sand (start at negative values) and clay (start at positive values) are following very similar patterns in each of the model’s factors, however the same spectral information is used inversely in the prediction. Factor 1 (dotted lines) represent the overall trend of the spectral contrast, mainly driven by the quartz Reststrahlen bands, since there are no other spectral features evident in the loading weights pattern (note that the distinct 8.65 μm feature of quartz is not considered in f1, f2, and f3). Factor 2 is already dominated by the spectral features of kaolinite (9, 9.8, 10.2, and 10.8 μm). Most of these kaolinite feature are being confirmed in factor 3, which also contains the clay feature at 8.3 μm. This also reveals the influence of the goethite feature just before 11 μm, which might be interfering with the clay minerals information in that region.