# Vis-NIR Spectroscopy and PLS Regression with Waveband Selection for Estimating the Total C and N of Paddy Soils in Madagascar

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## Abstract

**:**

^{2}), the root mean squared error of cross-validation (RMSECV), and the residual predictive deviation (RPD). Overall, ISE-PLS using first derivative reflectance (FDR) showed a better predictive accuracy than ISE-PLS for both TC (R

^{2}= 0.972, RMSECV = 0.194, RPD = 5.995) and TN (R

^{2}= 0.949, RMSECV = 0.019, RPD = 4.416) in the soil of Madagascar. The important wavebands for estimating TC (12.59% of all wavebands) and TN (3.55% of all wavebands) were selected from all 2001 wavebands over the 400–2400 nm range using ISE-PLS. These findings suggest that ISE-PLS based on Vis-NIR diffuse reflectance spectra can be used to estimate soil TC and TN contents in Madagascar with an improved predictive accuracy.

## 1. Introduction

^{−1}in recent decades despite relatively favorable water conditions, with 70% of rice-cropping areas categorized as irrigated in this country [32]. In a survey of several rice fields in Madagascar’s central highland, Tsujimoto et al. [33] showed a significant and linear response of rice yield against the soil organic carbon (SOC) content in relation to the N-supplying capacity of soils, which strongly indicates the importance of soil fertility management for increasing regional rice yields. Extensive research on SOC has been conducted using standard procedures, but most studies have focused on forest carbon stocks in the context of carbon dynamics, global warming, and environmental degradation in Madagascar [34,35,36,37,38]. Extensive and field-based soil C and N evaluations concerning the development of appropriate soil and nutrient management recommendations for the rice-cropping system, the country’s major land use, are limited.

## 2. Materials and Methods

#### 2.1. Study Site and Soil Sampling and Chemical Analyses

#### 2.2. Soil Chemical Analyses

#### 2.3. Vis-NIR Diffuse Reflectance Measurement

^{2}. A Spectralon (Labsphere, Inc., Sutton, NH, USA) reference panel (white reference) was used to optimize the ASD instrument prior to taking Vis-NIR reflectance measurements for each sample.

#### 2.4. Preprocessing of Spectral Data

#### 2.5. Standard Full-Spectrum Partial Least Sqares (FS-PLS) Regression

_{1}to x

_{i}are the surface reflectance or FDR values for spectral bands 1 to i (400, 401, …, 2400 nm), respectively; β

_{1}to β

_{i}are the estimated weighted regression coefficients; and ε is the error vector. The latent variables were introduced to simplify the relationship between the response variables and predictor variables. To determine the optimal number of latent variables (NLV), leave-one-out (LOO) cross-validation was performed to avoid over-fitting of the model, which was based on the minimum value of the root mean squared error of cross-validation (RMSECV) (see in Supplementary Materials: Figure S1). The RMSECV was calculated as follows:

_{i}and y

_{p}represent the measured and predicted soil parameters for sample i, respectively, and n is the number of samples in the data sets (n = 59).

#### 2.6. Iterative Stepwise Elimination Partial Least Squares (ISE-PLS) Regression

_{i}), described as follows:

_{i}is the standard deviation and β

_{i}is the regression coefficient; both s

_{i}and β

_{i}correspond to the predictor variable of the waveband i.

_{i}is evaluated, and the minimum values are eliminated as less informative wavebands. Subsequently, the PLS model is re-calibrated with the remaining predictors [44]. The model-building procedure is repeated until the final model is calibrated with the maximum predictive ability.

#### 2.7. Predictive Ability of the PLS Models

^{2}), RMSECV, and the residual predictive deviation (RPD) using LOO cross-validation. High R

^{2}and low RMSECV values indicate the best model for predicting the soil parameters. The RPD has been defined as the ratio of standard deviation (SD) of reference data for predicting RMSECV [45]. For the performance ability of calibration models, RPD was suggested to be at least 3 for agriculture applications, while RPD values between 2 and 3 indicate a model with a good prediction ability, 1.5 < RPD < 2 is an intermediate model needing some improvement, and an RPD < 1.5 indicates that the model has a poor prediction ability [13].

_{k}(a) is the importance of the kth predictor variable based on a model with a factors, W

_{ak}is the corresponding loading weight of the kth variable in the ath PLS regression factor, SSY

_{a}is the explained sum of squares of y obtained from a PLS regression model with a factors, SSY

_{t}is the total sum of squares of y, and m is the total number of predictor variables. A high VIP score indicates an important x-variable (waveband) [46,48].

## 3. Results and Discussion

#### 3.1. Soil Properties (TC and TN) and Their Correlations with Each Waveband

#### 3.2. Comparison between FS-PLS and ISE-PLS Models

^{2}values with iterative stepwise elimination procedures of redundant wavebands in the prediction of TC and TN using FDR. The RMSECV decreased as wavebands were removed but increased rapidly after more than 1749 and 1930 wavebands had been removed for TC and TN, respectively. Similarly, the R

^{2}value tended to increase slowly until the maximum value was obtained when 1749 and 1930 wavebands had been removed. The remaining 252 (=2001 − 1749) and 71 (=2001 − 1930) wavebands were considered useful wavelengths for estimating TC and TN, respectively. The selected number of wavebands (NW) and the selected NW as a percentage of the full spectrum (NW% = NW/whole waveband [N = 2001]) are presented in Table 2, with the values of NLV, R

^{2}, RMSEC/CV, and RPD from the FS-PLS and ISE-PLS models using the FDR dataset. The optimum NLV ranged between 7 and 15, determined as the lowest RMSECV values calculated from LOO cross-validation to avoid over-fitting of the model.

^{2}= 0.972, RMSECV = 0.194) and TN (R

^{2}= 0.949, RMSECV = 0.019), with RPDs of 5.995 and 4.416, respectively. Figure 4 shows the relationships between the observed and cross-validated predicted values of soil TC and TN from ISE-PLS using FDR data. These results indicate that the soil TC and TN can be rapidly and accurately predicted from Vis-NIR diffuse reflectance spectroscopy using PLS regression. Selecting a subset of wavebands related to soil chemical properties and removing unrelated wavebands further improved the PLS regression results. Moreover, based on RPD > 3, the quality and future applicability of our results could be considered to have an excellent predictive ability. The remaining NW (NW%) of TC and TN was 252 (12.59%) and 71 (3.55%), respectively, suggesting that over 87% of the waveband information from the soil reflectance spectrum was redundant and did not contribute to or disturb the prediction of soil TC and TN.

#### 3.3. Selected Wavebands from ISE-PLS Models

^{2}= 0.972, RMSECV = 0.194) than for TN (R

^{2}= 0.949, RMSECV = 0.019). Within the selected wavebands of soil TN (Figure 5), 90.1% (=64/71 bands × 100%) overlapped with the selected wavebands of soil TC, whereas different wavebands in TC calibration were revealed mainly in the NIR region (707, 717–719, 774 nm). These results indicated that TN prediction using our dataset was affected by strong correlations with TC data but might be directly estimated.

## 4. Conclusions

## Supplementary Materials

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) The setup used to measure the soil reflectance in a dark room; (

**b**) the use of a contact probe that touches the surface of the soil sample; and (

**c**) the five measuring spots on a soil sample.

**Figure 3.**Changes in RMSECV (black line) and R

^{2}values (red line) in models to estimate total carbon (TC) (

**a**) and total nitrogen (TN) (

**b**) with the stepwise removal of redundant wavebands. The minimum value of the root mean squared error of cross-validation (RMSECV) (blue dotted line) was obtained when 1749 and 1930 wavebands were removed for TC and TN, respectively.

**Figure 4.**Observed and predicted values of soil total carbon (TC) and soil total nitrogen (TN) contents using ISE-PLS models with first derivative reflectance (FDR) data (n = 59). The coefficient of determination (R

^{2}), root mean squared error of cross-validation (RMSECV), and residual predicted value (RPD) are cross-validated (leave-one-out cross-validation method) coefficient of determination, root mean squared error, and residual predictive values, respectively (see Table 2).

**Figure 5.**Soil reflectance and its first derivative reflectance (FDR) spectra for the total carbon (TC;

**a**) and total nitrogen (TN;

**b**) datasets and selected waveband (red bar) in iterative stepwise elimination of partial least squares (ISE-PLS) with variable importance in the prediction (VIP) score (blue line) from full-spectrum PLS (FSPLS) models.

Soil Parameters | n | Min | Max | Mean | SD | CV |
---|---|---|---|---|---|---|

TC (%) | 59 | 0.65 | 6.02 | 2.18 | 1.16 | 53.35 |

TN (%) | 59 | 0.06 | 0.44 | 0.17 | 0.08 | 48.08 |

**Table 2.**Optimum number of latent variables (NLV), coefficient of determination (R

^{2}), root mean squared errors of calibration (RMSEC) and cross-validation (RMSECV), and residual predictive values (RPD) from full-spectrum PLS (FS-PLS) and iterative stepwise elimination PLS (ISE-PLS) models with a selected number of wavebands (NW) and their percentages of the full spectrum (NW%).

Soil Parameter | Regression Method | Calibration | Cross-validation | NW | NW% | ||||
---|---|---|---|---|---|---|---|---|---|

NLV | R^{2} | RMSEC | R^{2} | RMSECV | RPD | ||||

Total carbon | FS-PLS | 14 | 0.996 | 0.076 | 0.893 | 0.379 | 3.064 | 252 | 12.59 |

(TC, %) | ISE-PLS | 12 | 0.995 | 0.084 | 0.972 | 0.194 | 5.995 | ||

Total nitrogen | FS-PLS | 9 | 0.960 | 0.016 | 0.837 | 0.033 | 2.480 | 71 | 3.55 |

(TN, %) | ISE-PLS | 7 | 0.974 | 0.013 | 0.949 | 0.019 | 4.416 |

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**MDPI and ACS Style**

Kawamura, K.; Tsujimoto, Y.; Rabenarivo, M.; Asai, H.; Andriamananjara, A.; Rakotoson, T. Vis-NIR Spectroscopy and PLS Regression with Waveband Selection for Estimating the Total C and N of Paddy Soils in Madagascar. *Remote Sens.* **2017**, *9*, 1081.
https://doi.org/10.3390/rs9101081

**AMA Style**

Kawamura K, Tsujimoto Y, Rabenarivo M, Asai H, Andriamananjara A, Rakotoson T. Vis-NIR Spectroscopy and PLS Regression with Waveband Selection for Estimating the Total C and N of Paddy Soils in Madagascar. *Remote Sensing*. 2017; 9(10):1081.
https://doi.org/10.3390/rs9101081

**Chicago/Turabian Style**

Kawamura, Kensuke, Yasuhiro Tsujimoto, Michel Rabenarivo, Hidetoshi Asai, Andry Andriamananjara, and Tovohery Rakotoson. 2017. "Vis-NIR Spectroscopy and PLS Regression with Waveband Selection for Estimating the Total C and N of Paddy Soils in Madagascar" *Remote Sensing* 9, no. 10: 1081.
https://doi.org/10.3390/rs9101081