Soil sampling and preparation were carried out by the soil laboratory “Laboratoire Sol-Eau-Plante” in Mali. Areas covered by the study are the administrative regions of Koulikoro and Sikasso where 755 and 122 samples, were collected respectively. The soil samples were collected from 0 - 10 cm depth. Figure 1 shows the geographical characteristics of each sampling site.

Soil reference data measurements were carried out in the soil laboratory “Laboratoire Sol-Eau-Plante” (LSEP) using standard laboratory methods. Soil samples were priory air dried, crushed and sieved to 2 mm. The total carbon was measured by an automatic titrator using the modified Anne method which is the oxidation of soil carbon by potassium dichromate. The available phosphorus of the soil was extracted with a combined solution of 0.1 M HCl and 0.03 M NH4F and the measurements were made using an ultraviolet (UV) spectrophotometer or a colorimeter. For the exchangeable K, the soil was leached with a 1 M ammonium acetate solution at pH 7. It was determined directly in the ammonium acetate percolate using a flame photometer.

The 877 soils samples were partitioned into two sub-samples constituting sets of calibration and validation. The selection was made in the way that all sampling sites are represented in both calibration and validation sets. Approximately 2/3 of samples from each sampling site are selected to form the calibration sample set (587 samples) and the remaining 1/3 is used to form the validation sample set (290 samples).

Spectral measurements and their processing were carried out at the Laboratory of Optics, Spectroscopy and Atmospheric Sciences (LOSSA). These measurements consist of recording the soils reflectance over the wavelength range of 342 - 1060 nm. Soils samples were priory air dried and crushed to pass a 2-mm sieve. A Miniature Fiber Optic Spectrometer working on UV-VIS-NIR spectral range (BLUE-Wave Miniature Fiber Optic Spectrometers for UV-VIS-NIR & OEM, StellarNet Inc.) was used to perform the spectral measurements. The spectrometer is connected to a PC on which the Spectra Wiz software is installed for controlling the data acquisition. The samples were scanned using a halogen tungsten

SL1 lamp source manufactured by StellarNet Inc. This light source has a wide spectral Range for 350 - 2500 nm-effective for color, reflectance, transmittance, and absorbance measurements. The Y-shaped optical fiber was used to transport light from the source to the sample and from sample to the spectrometer (Figure 2(a)) with the same incident angle of illumination.

Before being used, the raw spectral data are undergoing various pretreatments. The most common strategy for pre-processing spectra is to submit the raw data to one or more mathematical transformations intended to make them suitable for modeling.

Sample spectra were filtered using the RunMean function under “caTools” package of the R statistical software. The filtering consists in eliminating the interference related to the experimental conditions and the electronic noise of the measuring instrument.

Spectral reflectance was measured in the wavelength range of 342 - 1060 nm. Since the UV band is of a little interest for the soil spectral study, we have restrained the spectral band to 400 - 1000 nm with a spectral resolution of 0.5 nm. Figure 2(b) and Figure 2(c) shows the effect of filtering on the spectrum of a sample chosen randomly. The filtered spectra were then converted to spectral absorbance (A) using the following relationship:

A = log ( 1 / R ) (1)

where R is the actual spectral Reflectance.

The first part of the analysis is the calibration which consists of developing a mathematical model to determine the chemical properties Y (unknown concentration) from the available spectral measurements X (spectral absorbance). The model is setup using variable X and Y information of the calibration sample set. Once the model is established, it can be used to estimate the chemical properties of unknown samples. Two regressions models have been involved in this analysis: the principal component regression (PCR) and the partial least square regression (PLSR).

Validation is the second step of the analysis which consists in evaluating the performance of the calibrated model by comparing its estimates with the reference values. During this phase, the accuracy of the model is evaluated on a set of independent samples meaning samples that did not participate in the calibration process. Thus, a good prediction implies a good quality of the calibration model. If the model appears satisfactory, it can be applied in routine analysis to analyze unknown samples.

Both multivariate models were validated with an independent data set representing about 1/3 of the total sample. The models performances were assessed by using some standard statistics: coefficient of determination (R²), the Bias and the root mean square error (RMSE). These statistical measures were computed using the following formulations:

R 2 = ∑ i = 1 n ( y ^ i − y ¯ ) 2 ∑ i = 1 n ( y i − y ¯ ) 2 , B I A S = 1 n ∑ i = 1 n ( y i − y ^ i ) , R M S E = 1 n ∑ i = 1 n ( y i − y ^ i ) 2 (4)

With y ^ i the values of the measurements, y i the predicted values and y ¯ the average of the measurements.

By checking at all the statistical criteria R², Bias and RMSE, both models show

*STD: Standard deviation.

good calibration qualities. They have strong coefficients of determination and weak bias for all elements. The PCR gives the best calibration quality with R² stronger than 0.80 for all elements (Table 2). This performance is better than that found by [14] for the carbon, with R² = 0.68 in the NIR region (700 - 2498). The PLSR model also has good calibration quality with coefficients of 0.801 for potassium, 0.872 for carbon and 0.881 for phosphorus (Table 2).

However, the coefficient of determination is not the only parameter to be considered for assessing the performance of a model. The root mean square error and the Bias between the measured and predicted values are also used as statistics to evaluate the robustness of a model.

The RMSE obtained from the PCR method is 0.22, 1.00 and 0.17 respectively for carbon, phosphorus and potassium. And for the PLSR method, the RMSE is 0.21 for the C, 1 for the P and 0.15 for the K. The bias obtained from both models (0.0004 for C; 0.0017 for P and 0.0003 for K) are relatively weaker compared to their respective average values (0.51, 1.33 and 0.25).

These results can be further improved by proceeding to homogeneous distribution of the samples from different sampling sites, as some sampling sites are represented by nearly 60 samples while others sites had only 4 samples. It has been argued that the calibration of predictive models on a limited number of samples or on fairly homogeneous samples may limit the scope of the calibration model [15] .

It can be seen that the performance of the prediction models varies from one chemical property to another and also from one model to another. An independent validation of both multivariate models calibrated for the three chemical properties (C, K and P) reveals lower performance of prediction with regards to the cross-validation performance. The PCR model has coefficients of determination of 0.17 for carbon, 0.34 for potassium, and 0.50 for phosphorus (Figures 3(a)-(c)). These values are comparatively lesser than 0.87 (C) and 0.64 (K) obtained respectively by [16] with the band 1100 - 2500 nm and [17] with the band 400 - 2498 nm.

The independent validation of the PLSR method yielded R² = 0.29 for C, R² = 0.42 for K and R² = 0.57 for P (Figure 3(d), Figure 3(e), Figure 3(f)). Comparing

to some previous finding, these performances are lower compared to R² = 0.66 (C) and R² = 0.61 (K) obtained respectively by Sorensen and [18] with the band 408 - 2492 nm and [19] with the band 400 - 2498 nm. This low performance can be attributed to the wavelength band used and also to the large extension of the study area. Indeed, the predictions of the soil components by spectroscopy may fail if the samples are collected in a very large geographical area or from different morpho-pedological contexts. Some previous findings [20] explain the failure by the difference between the original soil parent materials. However, for the potassium, our result is better than R² = 0.40 obtained by [19] in the same conditions.

Although, for some chemical, the estimates gave low performances for both models, but it has to be noted that the PLSR assures qualities of prediction of the phenomenon better than the PCR. This is due to the fact that the PLSR components capture the information carried by the explanatory variables while paying attention to the link between the two variables.

The RMSE and the bias found are very low compared to the average of the reference data. For PCR, the RMSE obtained was 0.23 for C; 1 for P and 0.17 for K and the bias was 0.0125 for total carbon, 0.0709 for phosphorus and 0.002 for potassium. The PLSR model shows RMSE values of 0.22, 0.95 and 0.16, respectively for C, P and K; the respective biases found were −0.0108; 0.2023 and 0.009.