Prediction of Phosphorus Sorption Index and Availability by NIR and MIR in Soils in Madagascar

Abstract

The development of techniques for the rapid, inexpensive, and accurate determination of the phosphorus (P) availability and sorption index (PSI) in soils is important for P management in highly weathered tropical soils. The applicability of near- and mid-infrared reflectance spectroscopy (NIR and MIR) as tools for estimating P availability and PSI was assessed over a wide range of highly weathered soils in Madagascar. The predictions were based on chemometric methods using multivariate calibration models with partial least squares (PLS) regressions, and pedotransfer functions (PTFs). Chemometric methods failed to predict available P (P_resin). However, a P sorption index, determined as the P remaining in solution (P_rem), was estimated with acceptable accuracy with both NIR and MIR (R²_cv = 0.70 − 0.73; R²_v = 0.65 − 0.77; SEP(c) = 5.5 − 4.6 mg kg⁻¹). The PTFs showed that the PSI was well explained by iron oxide, gibbsite, and sand contents, all of these compounds being well predicted by NIR or MIR (R²_v > 0.70). These results indicate that NIR and MIR can be helpful for a rapid estimate of PSI of highly weathered ferralitic soils.

1. Introduction

Phosphorus (P) is one of the main growth-limiting nutrients for plants. The lack of adequate levels of available P in soils is one of the major constraints for crop production in tropical soils, e.g., in Madagascar [1]. Consequently, crop yields remain low and far below their potential. Soil P deficiency may be due to the low P-status of the parent material, soil weathering, mismanagement through imbalance between nutrient input and export by harvested products and loss of P, e.g., through soil erosion. Moreover, many tropical soils are marked by a high P-fixing capacity. These soils have a predominance of 1:1 clay minerals, such as kaolinite, iron (Fe), and aluminum (Al) oxides. These minerals have a particularly strong affinity for the phosphate ion [2,3]. Whereas the demand for P is predicted to increase by 50–100% by 2050 to meet increasing nutritional demand, phosphate reserves will be depleted in 50–100 years [4]. Although this pessimistic view is not shared by all [5], corrective fertilization of soils with large amounts of phosphate fertilizers is not feasible in most African countries. Thus, improving P use efficiency in highly weathered P-sorbing tropical soils is of great concern.

There are a number of standard chemical methods for the determination of available soil P (e.g., Bray, Mehlich, Olsen; see [6], and references cited therein). Depending on soil types or previous fertilization history, these indexes often fail to satisfactorily predict P availability [7]. In fact, these chemical methods dissolve P-forms not readily available for plants in proportions that vary with the nature and duration of the extraction, the type of soil, and the history of fertilization [8]. However, in many countries, recommendations for fertilizer P application are based on such P availability index. Phosphorus sorption or desorption methods have also been used for measuring fast and reversible P sorption [9]. As the soil solution only contains about 1% of the uptake by the crop, this means that 99% of the P is replenished from the solid constituents of the soil. So, according to Barrow [10], the measurement of adsorption/desorption is also useful to predict the amount of fertilizer needed for plant growth. In acidic soils, the Al and Fe minerals are key constituents of sorption processes. Desorption of soil P by anion-exchange resins mimics the process of P uptake by plant roots, which makes this method one of the most applied methods to assess plant-available P [9]. The P sorption in soils has traditionally been evaluated by the P buffer capacity (PBC; [11]), i.e., determined as the slope of the P sorption curve, which provides a useful tool for improved management of P in agricultural systems [12,13]. A simple, single-addition P-sorption index (PSI) was successfully developed as a surrogate of PBC in Australian and Brazilian soils [14,15].

For a few years, near- and mid-infrared spectrometry (NIR, in the wavelength range 1100–2500 nm, and MIR, in the wavelength range 2500–25,000 nm) have been used extensively for the prediction of various soil properties [16,17,18]. Various studies focus on the determination of the potentially available P fractions or on the ability of soil to bind P (P sorption). With a few exceptions of soil sets representing special or unusual conditions, most predictions of extractable P in soils resulted either in low R² values (0.5–0.7) for calibration or were considered to be completely unreliable (R² < 0.50) [18,19]. However, some successful models for South African and Australian soils were reported for PBI by using NIR or MIR spectroscopy, with prediction R² values ranging from 0.69 to 0.87 for calibration (see [20]). Recent results also showed the potential of MIR spectrometry to predict PSI for temperate soils [21]. Success in predictions of P sorption by infrared spectroscopy may be attributed to the response of the infrared spectra to the soil components in the soil matrix that present a great affinity for phosphate anions (i.e., some minerals such as Al- and Fe-oxyhydroxides and carbonates, SOM/Al complexes) [18].

According to Minasny et al. [22], P adsorption capacity can be predicted from clay content, pH, and soil color, using pedotransfer function (PTF), i.e., a relationship between soil parameters and the easier measurable properties usually available from routine soil analysis. Aluminum and iron oxide fractions, such as oxalate-extractable aluminum and iron and dithionite-extractable iron [23], have also been found to be useful predictors. As the predictions of soil minerals using spectral methods have been found to be effective in highly weathered tropical soils [24,25], NIR and MIR spectrometry can be useful tools to predict some of the mineralogical properties of the soils and use them in PTF.

The main objective of this study was to investigate the use of NIR and MIR spectroscopy to predict the desorption of soil P, using anion-exchange resins (P_resin), and sorption of soil P, using single-addition P-sorption index (PSI), over a wide range of highly weathered soils in Madagascar. We also built pedotransfer functions for predicting PSI and compared the usefulness of applying spectrally predicted soil parameters in the PTFs, that could be used as a complementary tool to standard chemical methods.

2. Materials and Methods

2.1. Soil Sampling and Analysis

A set of Malagasy soils, described in a previous study [25], was used for this study. Briefly, highly weathered soils, classified as Ferralsols, Cambisols, and Nitisols [26], were collected at 120 sites in Madagascar (Figure 1). At each site, composite samples were taken at 0–0.1, 0.1–0.2, 0.2–0.3, 0.5–0.6, and 0.8–0.9 m depth, resulting in 600 soil samples.

The spectra of the 600 samples were acquired, and 148 of those were selected from all the five soil horizons, according to their NIR spectral representativeness, and analyzed by reference methods.

For P_resin extraction, one 6 cm² strip of anion exchange membrane in bicarbonate form (Product 55164 2S; BDH Laboratory Supplies, Poole, England, anion exchange capacity: 0.037 cmol_c cm⁻²) was shaken with 2 g of soil and 30 mL of deionized water on an end-over-end shaker at 25 °C for 16 h. The resin strip was removed and washed. The phosphate extracted by the resin was eluted by shaking for 30 min with 30 mL 0.1 M NaCl/0.1 M HCl. The PSI was determined after a single addition of 60 mg P L⁻¹ (as KH₂PO₄) in 0.01M CaCl₂ added at a 1:10 soil:solution ratio [27]. The suspensions were equilibrated by shaking in an end-over-end shaker at 25 °C for 16 h. After equilibrium, P remaining in solution (P_rem) was determined. Total soil P (P_total) was determined after digestion of 0.1 g of soil with 2 mL HClO₄ at 205 °C for 2 h. The extracted orthophosphate was determined spectrophotometrically using the blue molybdate-ascorbic acid method.

Total C was analyzed by dry combustion in a LECO model CHN 600 (Leco Corp., St Joseph, MI, USA). The soil pH was measured in distilled water (pH_water) using a 1:2.5 (mass) soil:solution ratio. The particle size distribution was determined with the pipette method after dispersing with 1 M NaOH.

Iron oxides were dissolved using the citrate-bicarbonate-dithionite (CBD) deferrification method of Mehra and Jackson [28]. The Fe₂O_3cbd content represents the amount of free iron oxide components of soils. The kaolinite (Kt), gibbsite (Gb), goethite (Gt), and hematite (Hm) contents were computed according to the methodology of Reatto et al. [29] after digestion with sulphuric acid (SA) (1:1 distilled water/conc. H₂SO₄ volume ratio) (see [24,25,29], for details).

2.2. NIR and MIR Spectrometry

The reflectance of the soil samples was determined in the near-infrared region using a Foss NIRSystems 5000 spectrophotometer (Silver Spring, MD, USA) and in the mid-infrared region using a Nicolet 6700 spectrophotometer (Thermo Fisher Scientific Instruments, Madison, WI, USA). For NIR spectrometry, approximately 5 g of finely ground soil (<200 µm), packed into a 5 cm diameter ring cup with a quartz window, was scanned in the 1100 to 2498 nm range with a resolution of 2 nm. MIR analyses were subsequently performed on the same samples. The reflectance was measured over the range of 400–4000 cm⁻¹ (2500–25,000 nm) with a spectral resolution of 3.86 cm⁻¹. Each sample spectrum was averaged from 15 spectra for NIR and 25 for MIR. Data were analyzed using the WinISI III–V 1.63e software (Foss NIR Systems/TecatorInfrasoft International, LLC, Silver Spring, MD, USA).

Among the 148 representative samples, we used PCAs (principal component analysis) to look for the best cluster of data and to select independently the sets of calibration and validation for NIR and MIR. The best PCAs were calculated using SNVD 2441 for NIR and SNVD 0441 for MIR. This resulted in different calibration and validation sets for NIR and MIR, with, respectively, 104 and 42 samples (2 outliers) for calibration and validation sets for NIR, and 104 and 41 samples (3 outliers) for calibration and validation sets for MIR. NIR and MIR multivariate calibration models were performed as described previously [25], using modified partial least squares regression (mPLS). The spectral pre-processing techniques used included no pre-processing (NONE), multiplicative scatter correction (MSC), standard normal variate (SNV), detrending (DETREND), and SNV with detrending (SNVD). The four successive numbers corresponded to the derivatives (0, 1, and 2: no derivation, first and second derivatives, respectively), the number of point gaps (0, 4, 5, 10), the number of points for first smoothing (1, 4, 5, 10), and the number of points for second smoothing (always 1). The mPLS regression was achieved using 15 and 25 mPLS factors for NIR and MIR, respectively. The numbers of mPLS factors were determined by minimizing the standard error of cross-validation over the calibration sets.

The performance of the calibration model was assessed using the coefficient of determination of cross-validation (R²_cv) and the ratio of performance to deviation (RPD_cv), which is the ratio of standard deviation to the standard error of cross-validation (SECV), and was considered acceptable for RPD_cv > 2, and R²_cv > 0.75 [30,31]. The prediction accuracy of the model was evaluated on the validation subset (which had not been used for model development), using the validation R²_v and RPD_v.

We analyzed the kaolinite and gibbsite by specific diagnostic absorption peaks in the NIR range at around 2205 nm for kaolinite and 2265 nm for gibbsite [25,32]. Data processing was performed by R software with packages xlsx, car, FacToMineR, lattice, Mass, leaps, Hmisc et ade4 [25].

2.3. Calibration of Pedotransfer Functions

Pedotransfer functions were built for the prediction of P_resin and P_rem as a function of mineralogical and physico-chemical soil properties. Stepwise multiple linear regression analysis was carried out with the R software with packages xlsx, car, FacToMineR, lattice, Mass, leaps, Hmisc et ade4 for establishing a function in which P_resin or P_rem were dependent variables on the other determined soil properties as independent variables. PTF models were built to relate P_resin and P_rem (i) to the chemically measured mineralogical (Kt, Gb, Fe₂O_3cbd) and physico-chemical (pH_water, C, clay, silt, sand) covariates and (ii) to the mineralogical and physico-chemical covariates predicted by NIR or MIR spectrometry (all except pH_water).

3. Results

3.1. Reference Soil Analysis

The mean values, standard deviation, and variation range are shown in

Table 1. Summary statistics for constituents and physico-chemical properties of the ferrallitic soils studied.

Constituent	Unit	Min	Max	Mean	SD	Median
Kt 1	g kg−1	13.3	676.3	304.7	147.9	288.3
Gb 2	g kg−1	0.0	456.2	109.9	116.9	83.8
Fe2O3cbd 3	g kg−1	0.0	181.4	42.4	30.5	37.2
Clay	g kg−1	1.4	766.1	332.1	151.0	342
Silt	g kg−1	20.2	566.0	216.3	122	188
Sand	g kg−1	42.6	901.6	451.6	199.1	442.8
C 4	g kg−1	1.2	85.5	14.0	12.9	10.2
pHwater		2.4	7.1	5.5	0.6	5.5
Ptot 5	mg kg−1	12.7	1955.4	374.3	318.5	259.6
Presin 6	mg kg−1	0.0	4.4	0.8	0.9	0.4
Prem 7	mg kg−1	1.2	47.4	23.1	9.5	22.8

¹ Kaolinite; ² gibbsite; ³ amount of Fe determined by the CBD method; ⁴ carbon; ⁵ phosphorus total; ⁶ phosphorus available; ⁷ phosphorus remaining in solution.

for mineralogical characteristics, particle size distribution, and chemical characteristics of the soils. A large variability was observed in the studied soils. Kaolinite was the dominant mineral of the clay fraction (305 ± 148 g kg⁻¹) followed by gibbsite (110 ± 117 g kg⁻¹) (Table 1). Crystalline iron oxides, estimated by CBD extraction (Fe₂O_3cbd), amounted to 42 ± 31 g kg⁻¹. The most common textural classes among all soil samples were coarse-loam to clay. The clay content ranged from 1 to 766 g kg⁻¹ with a mean of 332 ± 151 g kg⁻¹. The silt and sand means were 216 ± 122 and 451 ± 199 g kg⁻¹, respectively. These values are quite similar to those of Grinand et al. [33] who found 300, 161, and 517 g kg⁻¹ for clay, silt, and sand, respectively, for a large database (618 samples) of soils from Madagascar. The total C content of the soils varied from 1.2 to 85.5 g kg⁻¹, with mean values of 14.0 ± 12.9 g kg⁻¹, also very close to those of Grinand et al. [33], i.e., 11.8 ± 7.2 g kg⁻¹. The soils were generally acidic, with a mean pH_water of 5.5 ± 0.6.

The total (P_total), available (P_resin), and remaining (P_rem) P contents varied considerably among samples (Table 1), with ranges of 13–1955, 0–4.4, and 1.2–47.4 g kg⁻¹, respectively. The means for P_tot, P_resin, and P_rem were 374 ± 319, 0.8 ± 0.9, and 23.1 ± 9.5 mg kg⁻¹, respectively. The low availability of P (P_resin) is similar to that observed in other soils [1] and explains the P deficiencies generally observed in soils of the Highlands in Madagascar [34].

3.2. NIR and MIR Prediction of Soil Variables through Chemometric Approach

Prediction of soil phosphorus using both NIR and MIR spectrometry based on multivariate regression through principal components and partial least squares approaches were poorly effective (

Table 2. Calibration and validation statistics of soil phosphorus properties, using NIR and MIR.

			Calibration Set
Constituent	Unit	Preprocessing	N 6	Out 7	n1 8	Mean	SD 9	SECV 10	R²cv 11	RPDc 12
NIR
Ptot 1	mg kg−1	None 4 2441 *	104	4	100	318.8	230.8	193.5	0.30	1.2
Presin 2	mg kg−1	None 1441 *	104	5	99	0.8	0.9	0.6	0.56	1.5
Prem 3	mg kg−1	None 1441	104	4	100	24.0	9.1	5.0	0.70	1.8
MIR
Ptot 1	mg kg−1	None 1441	104	6	98	352.3	256.4	167.0	0.57	1.5
Presin 2	mg kg−1	Snvd 5 1441	104	8	96	0.7	0.8	0.6	0.43	1.3
Prem 3	mg kg−1	Snvd 0011 *	104	3	101	23.3	9.5	5.0	0.73	1.9
			Validation Set
Constituent	Unit	Preprocessing	n2 13	Mean	SD	SEP(c) 14	Bias	Slope	R²v 15	RPDv 16
NIR
Ptot 1	mg kg−1	None 2441	42	321.2	136.2	261.9	34.5	1.1	0.26	1.2
Presin 2	mg kg−1	None 1441	42	0.8	0.8	3.8	0.4	0.5	0.01	1.0
Prem 3	mg kg−1	None 1441	42	24.0	8.0	5.5	−0.4	0.9	0.65	1.7
MIR
Ptot 1	mg kg−1	None 1441	41	366.84	255.5	210.1	23.3	1.0	0.60	1.6
Presin 2	mg kg−1	Snv 1441	41	0.7	0.8	7.1	1.0	1.0	0.0.1	1.0
Prem 3	mg kg−1	Snvd 0011	41	23.2	8.5	4.6	−0.1	1.0	0.77	2.1

¹ Total phosphorus; ² phosphorus available; ³ phosphorus remaining in solution; ⁴ no preprocessing; ⁵ standard normal variate and detrend; * the numbers indicate the derivatives (0, 1, and 2: no derivation, first and second derivatives, respectively)—number of point gap (0, 4)—number of points for first smoothing (1, 4) and number of points for second smoothing (1); ⁶ total number of sample; ⁷ number of outliers; ⁸ number of samples in the calibration set (N—out); ⁹ standard deviation; ¹⁰ standard error of cross-validation; ¹¹ coefficient of determination of cross-validation that corresponds to the percent of variation described in the data; ¹² ratio performance deviation of cross-validation (SD/SECV); ¹³ number of samples in the validation set; ¹⁴ standard error of prediction corrected; ¹⁵ coefficient of determination of SEP; ¹⁶ 1/[racine (1 − R²)].

). Only P_rem was satisfactorily calibrated, according to the classification of Chang et al. [30] and Malley et al. [31], with R²_cv = 0.70 and 0.73, and RPD_cv = 1.8 and 1.9, respectively, for NIR and MIR spectrometry. The R²_v were similar (0.65–0.77), with SEP(c) = 5.5–4.6) making it usable for prediction. The predictions of P_resin and P_tot were unsatisfactory (R²_v < 0.40).

Calibration and validation statistics of physico-chemical and mineralogical soil properties, using mPLS methods on NIR and MIR spectra, were presented in

Table 3. Calibration and validation statistics of physico-chemical and mineralogical soil properties, using NIR and MIR.

			Calibration Set
Constituent	Unit	Preprocessing	N 10	Out 11	n1 12	Mean	SD 13	SECV 14	R²cv 15	RPDcv 16
NIR
Kt 1	g kg−1	None 5 2441 *	104	5	99	309.3	147.8	95.0	0.60	1.6
Gb 2	g kg−1	None 0011 *	104	34	70	138.4	107.07	67.8	0.60	1.6
Fe2O3cbd 3	g kg−1	Msc 6 2551 *	104	9	95	36.9	26.0	11.8	0.80	2.2
C 4	g kg−1	None 1441 *	104	4	100	1.3	1.1	0.5	0.79	2.1
Clay	g kg−1	None 0011 *	104	4	100	311.4	136.4	97.7	0.49	1.4
Silt	g kg−1	Snv 7 1441 *	104	3	101	211.0	127.2	99.0	0.39	1.3
Sand	g kg−1	Snv 1441	104	4	100	480.1	196.3	127.9	0.58	1.5
pHwater		Snv 2441 *	104	4	100	5.46	0.4	0.3	0.37	1.3
MIR
Kt	g kg−1	None 0011	104	6	98	298.9	140.1	90.3	0.59	1..6
Gb	g kg−1	None 0011	104	25	79	149.4	116.2	78.4	0.54	1.5
Fe2O3cbd	g kg−1	Detrend 8 1441	104	6	98	40.9	25.6	16.7	0.57	1.5
C	g kg−1	Snvd 9 1441	104	7	97	1.1	0.9	0.3	0.85	2.6
Clay	g kg−1	Snv 210101 *	104	6	98	349.4	131.1	87.3	0.56	1.5
Silt	g kg−1	Snv 2551	104	4	100	218.2	116.6	76.5	0.58	1.5
Sand	g kg−1	Snv 0011	104	2	102	441.2	186.9	110.0	0.66	1.7
pHwater		Snvd 0011	104	7	97	5.5	0.4	0.4	0.24	1.1
			Validation Set
Constituent	Unit	Preprocessing	n2 17	Mean	SD	SEP(c) 18	Bias	Slope	R²v 19	RPDv 20
NIR
Kt	g kg−1	None 2441	42	301.2	127.1	125.5	−28.0	0.7	0.37	1.3
Gb	g kg−1	None 0011	42	184.3	92.9	83.5	10.5	0.9	0.51	1.4
Fe2O3cbd	g kg−1	Msc 2551	42	52.3	27.2	21.3	1.4	1.0	0.63	1.6
C	g kg−1	none 1441	42	1.5	0.8	0.4	−0.2	0.9	0.81	2.3
Clay	g kg−1	None 0011	42	348.4	74.6	114.6	49.3	1.1	0.33	1.2
Silt	g kg−1	Snv 1441	42	226.8	99.9	132.4	−18.8	0.1	0.02	1.0
Sand	g kg−1	Snv 1441	42	431.6	133.1	143.7	−37.3	0.9	0.40	1.3
pHwater		snv 2441	42	5.5	0.3	0.7	0.2	1.5	0.27	1.2
MIR
Kt	g kg−1	None 0011	41	312.3	93.1	126.4	8.5	0.9	0.30	1.2
Gb	g kg−1	None 0011	41	121.5	78.0	67.8	11.9	0.8	0.45	1.3
Fe2O3cbd	g kg−1	Detrend 1441	41	38.9	24.6	22.5	5.7	1.4	0.72	1.9
C	g kg−1	Snvd 1441	41	1.4	0.9	0.4	0.0	1.0	0.87	2.8
Clay	g kg−1	Snv 210101	41	328.2	105.6	117.5	6.2	1.2	0.55	1.5
Silt	g kg−1	Snv 2551	41	232.5	119.4	107.4	−39.6	0.5	0.32	1.2
Sand	g kg−1	Snv 0011	41	442.4	177.5	115.4	30.3	1.0	0.76	2.0
pHwater		Snvd 0011	41	5.4	0.3	0.5	0.1	1.2	0.38	1.3

¹ Kaolinite; ² gibbsite; ³ amount of Fe determined by the CBD method; ⁴ carbon; ⁵ no preprocessing; ⁶ multiplicative scatter correction; ⁷ standard normal variate; ⁸ removes of linear and quadratic curvature of each spectrum; ⁹ standard normal variate and detrend; * the numbers indicate the derivatives (0, 1, and 2: no derivation, first and second derivatives, respectively)—number of point gaps (0, 4, 5, 10)—number of points for first smoothing (1, 4, 5, 10) and number of points for second smoothing (1); ¹⁰ total number of sample; ¹¹ number of outliers; ¹² number of samples in the calibration set (N—out); ¹³ standard deviation; ¹⁴ standard error of cross-validation; ¹⁵ coefficient of determination of cross-validation that corresponds to the percent of variation described in the data; ¹⁶ ratio performance deviation of cross-validation (SD/SECV); ¹⁷ number of samples in the validation set; ¹⁸ standard error of prediction corrected; ¹⁹ coefficient of determination of SEP; ²⁰ 1/[racine (1 − R²)].

. The accuracies of the prediction of the carbon content of the soils were considered successful using NIR (R²_cv = 0.79 and RPD_cv = 2.1) and excellent using MIR (R²_cv = 0.85 and RPD_cv = 2.6). For mineralogy and texture, most of the predictions resulted in lower R² values (0.5–0.7), for both NIR and MIR. The best predictions were obtained for Fe₂O_3cbd with NIR (R²_cv = 0.80 and RPD_cv = 2.2) and sand (R²_cv = 0.66 and RPD_cv = 1.7) with MIR. The prediction of the main minerals of the soils, i.e., kaolinite and gibbsite, had R²_c values between 0.5–0.6 and R²_v still lower. However, in a previous paper on the same soils [25], we got satisfactory coefficients of determination for gibbsite and kaolinite, with adjusted R²_cv = 0.71 and 0.69, respectively, and similar results for the calibration set, using the height of the second derivative of NIR specific spectral peaks situated at nearly 2205 nm for kaolinite and 2265 nm for gibbsite. The pH_water predictions were completely unreliable (R²_cv < 0.40) (Table 3).

3.3. Development of a PTF for Soil Phosphorus Using other Soil Variables Prediction through Chemometric Approach

Simple regression statistics (

Table 4. Pearson coefficients and significance levels for correlation between physico-chemical and mineralogical soil properties and P_rem or P_resin of the ferrallitic soils studied.

		Prem 5 (mg L−1)		Presin 6 (mg L−1)
Variables	Unit	Coefficient	Significance Level	Coefficient	Significance Level
Kt 1	g kg−1	0.0277	0.7380	−0.050	0.5450
Gb 2	g kg−1	−0.586	0.0000	−0.019	0.8230
Fe2O3cbd 3	g kg−1	−0.488	0.0000	−0.097	0.2430
pHwater		0.120	0.1470	0.482	0.0000
Clay	g kg−1	−0.533	0.0000	0.010	0.9080
Silt	g kg−1	−0.167	0.0423	0.260	0.0014
Sand	g kg−1	0.507	0.0000	−0.167	0.0431
C 4	g kg−1	−0.284	0.0005	−0.025	0.7600

¹ Kaolinite; ² gibbsite; ³ amount of Fe determined by the CBD method; ⁴ carbon; ⁵ phosphorus remaining in solution; ⁶ phosphorus available.

) indicated a significant linear relationship between P_rem and C, clay, silt, sand, Fe₂O_3cbd, and Gb, whereas pH_water and Kt were not significantly related to P_rem. Among the different soil properties, gibbsite content was the most closely and significantly correlated with P_rem (r = −0.59). The amount of crystallized oxides was also significantly correlated with P_rem (r = −0.49), however, the relationship with gibbsite was better than with iron oxides. Strong relationships between P_rem and the clay (r = −0.53) and sand (r = 0.51) contents were observed, with a negative coefficient for the former and a positive one for the latter. The clay fraction was highly correlated to gibbsite and iron oxide contents (r = 0.35 and 0.54, respectively) which also had significant negative correlations with P_rem. The sand fraction behaved opposite to the clay fraction. The C content was negatively correlated with P_rem, which was a surprising result, because organic matter is supposed to reduce phosphorus retention [35], and thus increase P_rem. Soil minerals (kaolinite, gibbsite, iron oxides) play a key role in the stabilization of organic matter [36] and thus explain the significant correlation between C and Gb (r = 0.24). The chemical reaction of the soil (pH_water) does not seem to contribute much to the sorption of P, in line with the review paper of Gérard [3], explaining that the binding capacity of Fe/Al oxides varies moderately in the pH range of Madagascar soils. Regression between P_resin and soil properties showed that pH_water, silt, and sand contents were the only significant variables (Table 4).

The multiple regression analyses developed are presented in

Table 5. Best-fit multiple regression analyses for P_rem or P_resin of the ferrallitic soils studied using chemically analyzed or values predicted using spectrometry (except pH).

Variables	Multiple Regression Equation		R2c	RMSE
	Chemically analyzed variables
Prem	Prem = 22.32 + 1.55 pHwater − 0.127 C − 0.009 Kt − 0.039 Gb − 0.065 Fe2O3cbd + 0.008 S	(1)	0.52	6.49
	Prem = 25.78 − 0.13 C − 0.031 Gb − 0.062 Fe2O3cbd + 0.012 S	(2)	0.49	6.69
	Prem = 25.61 − 0.035 Gb − 0.072 Fe2O3cbd + 0.010 S	(3)	0.46	6.89
Presin	Pres = −0.208 + 0.053 C − 0.001 Gb + 0.001 S	(4)	0.42	0.70
	Pres = 0.284 + 0.001 S	(5)	0.05	0.90
	Spectrally predicted variables
Prem	Prem = 20.79 + 1.285 pHwater − 0.290 C − 0.007 Kt − 0.029 Gbcbd − 0.105 Fe2O3cbd + 0.020 S	(6)	0.50	6.61
	Prem = 24.897 − 0.261 C − 0.027 Gb − 0.099 Fe2O3cbd + 0.019 S	(7)	0.49	6.72
	Prem = 24.160 − 0.030 Gb − 0.111 Fe2O3cbd + 0.015 S	(8)	0.43	7.09
Presin	Pres = 0.847 + 0.058 C − 0.001 Kt − 0.001 Gb − 0.007 Fe2O3cbd	(9)	0.41	0.71
	Pres = 1.777 − 0.002 Kt − 0.002 Gb − 0.007 Fe2O3cbd	(10)	0.20	0.84

P_rem: phosphorus remaining in solution; P_resin: phosphorus available; C: carbon; Kt: kaolinite estimated after extraction with sulfuric acid; Gb: gibbsite estimated after extraction with sulfuric acid; Fe₂O_3cbd: amount of Fe determined by the CBD method; S: sand; R²_c: coefficient of determination of calibration; RMSE: root mean square error.

, and illustrated graphically in Figure 2 for P_rem. For chemically analyzed variables, the strongest multiple regression (p < 0.0001) for P_rem included five factors (each significant at p-value = 0.05), representing pH_water, texture, and mineralogy variables (Equation (1); Figure 2a). As expected, given their P sorption capacity, Fe/Al oxides (i.e., Gb and Fe₂O_3cbd) had a major effect on P_rem. The sand content (i.e., quartz), known for not having significant sorption capacity for P, counteracted the effects of Fe/Al oxides and was useful for the accurate prediction of P_rem. The pH_water, which was not correlated with P_rem (Table 4), was removed without a substantial reduction of the model efficiency (Equation (2)). The C content had significant contributions (Equation (1)); however, its inclusion in the model improved only the explanation of variability marginally (Equation (3); Figure 2b), presumably, because of the collinearity of C with Al oxides (r = 0.24). The root-mean-square error (RMSE) was between 6.5 and 6.9 mg L⁻¹, depending on the models. A multiple regression equation was also obtained for P_resin (R² = 0.42, Equation (4)) using the same five factors as for P_rem, but the efficiency of the model was greatly reduced after removing pH_water and C content (R² = 0.05, Equation (5)). The goodness of fit of multiple regressions was lower for P_resin than for P_rem (Table 5).

We tested the same multiple regression analyses using the variables predicted with the PLS methods (carbon, Fe₂O_3cbd, sand) and with the NIR models proposed by Ramaroson et al. [25] for kaolinite and gibbsite. For pH_water, we used measured values as it could not be predicted with spectral methods. For P_rem, the multiple regression equations were approximately of the same quality as those obtained with only the measured variables (Equations (7) and (8) in Table 5; Figure 2c). Moreover, the relationship between P_rem predicted using chemically measured data (Equation (3)) and P_rem predicted with PTF using spectrally predicted data (Equation (8)) was good (slope = 0.83; R² = 0.74) (Figure 3).

4. Discussion

4.1. Use of Infrared Spectroscopy to Develop P Availability Indices with Chemometric Methods

Phosphorus is an essential nutrient required by crops in large amounts. Soil testing is one of the most cost-effective nutrient management tools available to farmers and crop advisers. Soil tests provide an index of the labile plant-available P by extracting a fraction of the P that is related to the yield response of crops [37]. However, these indexes often fail to satisfactorily predict P availability [6,7].

Soriano-Disla et al. [18] have reviewed the performance of visible, near-, and mid-infrared reflectance spectroscopy for the prediction of soil physical, chemical, and biological properties using multivariate chemometric regression modeling. For P availability indices, with few exceptions of soil sets representing special or unusual conditions, most predictions of extractable P in soils resulted either in low R²_v values (0.5–0.7) or were considered to be completely unreliable (R² < 0.50). At regional or country scales, most of the results are unreliable with both NIR [24,30] and MIR [20,22,38]. An exception was reported by Morón and Cozzolino [39] who found low accuracy prediction, using NIR, for resin and Bray extractable P (R²_v = 0.61 and 0.58, respectively) for soils from Uruguay. Our results, presenting even lower coefficients (R²_v = 0.06 for NIR and 0.36 for MIR), are comparable to the majority of studies conducted on a similar scale.

Sorption of P in the soil controls its chemical mobility and bioavailability [40]. The ability of soil to bind phosphorus (P sorption) can be also a useful index of P availability. Good predictions were reported in the study of Soriano-Disla et al. [18] for P sorption with MIR (moderately successful predictions, median R²_v = 0.83). However, the number of studies and geographic area studied (i.e., west Australia) are very limited [20,22,41]. Dunne et al. [21] also showed moderately successful predictions (R²_v up to 0.67) using different sorption models, i.e., single point sorption index, Langmuir sorption isotherm, and Freundlich sorption isotherm, the P sorption index determined as the P remaining in solution being the most successful. Studies using vis-NIR were less successful (R²_v = 0.69) [42]. Our results showed nearly the same accuracy of prediction, with R²_v = 0.65 and 0.77 for NIR and MIR, respectively, as the reported studies. However, these predictions could be used as acceptable soil quality indices for evaluating soil quality or fertility by African farmers who have no access to soil analysis due to high prices.

4.2. Use of PTF to Relate P Availability Indices to Soil Properties

The extent to which a soil adsorbs P (sorption capacity) differs widely among different soils. Factors controlling phosphate binding in soils have been the focus of research efforts in recent decades (e.g., [3,43]). P sorption tends to be high in soils with a high proportion of small-size particles such as clay and, hence, high specific surface area [43]. Aluminum and iron oxides are considered the main phosphate adsorbents in soils ([3] and references therein). Accordingly, close relationships were found between the amounts of adsorbed phosphate and certain aluminum and iron forms (crystalline and amorphous), which lead to the creation of pedotransfer functions for predicting adsorbed phosphate [23]. Crystalline Fe and Al oxides generally provide a large part of the P sorption capacity of highly weathered soils [44], while amorphous Fe and Al oxides contribute to the sorption of P by less weathered soils [23]. However, the amount of amorphous oxides is low with regards to crystalline ones, and, to our knowledge, it is not possible to quantify them independently by NIR or MIR. A substantial contribution of kaolinite to phosphate sorption has been also demonstrated recently [3]. The effect of pH and organic matter on phosphate sorption by clay minerals and Fe/Al oxides has been also extensively studied [35,45]. Briefly, soluble humic molecules and organic acids can be sorbed to Al and Fe oxide surfaces consequently blocking P adsorption sites, then decreasing P sorption and increasing P availability.

Chemical properties that are related to the mineral and organic components can be predicted spectrometrically because of the interaction between the soil properties and the active soil components: organic matter, clay minerals, and oxides [46]. Therefore, adsorption-desorption reactions, such as P availability or P sorption, can be predicted if quantitative mineralogy and chemical analysis of various properties are available. However, detailed mineralogical measurements and some specific analyses are expensive and rarely made in soil surveys. There exist a few PTFs that relate P sorption to aluminum and iron oxide contents [23]. Our results showed that, in addition to Fe/Al oxides, sand and carbon content are key parameters. These compounds have been predicted with a relatively good accuracy [18]. Demattê et al. [47] and Vendrame et al. [24] demonstrated the use of NIR spectroscopy for identifying major soil mineralogy in tropical soils from Brazil. Numerous studies have reported accurate predictions of soil total C and N content (e.g., [16,48,49]). Accurate calibration for sand using MIR or combined vis-NIR has been found, with R²_v between 0.70 and 0.99 [24,30,38,50,51].

Our results are in the range of most published results with reliable spectroscopy-based soil analysis for soil compounds used in our PTF, with R²_v of 0.87 for C (with MIR and PLS calibration); 0.76 for sand (MIR-PLS); 0.72 for Fe₂O_3cbd (MIR-PLS); and 0.75 for gibbsite (NIR, height of the first derivative of specific peak at 2265 nm) (Table 3 and Figure 2.). The fit of multiple regression analyses for P_rem or P_resin, using data obtained by chemical analyses and predicted values through spectrometry, were similar (Table 5), and a good relationship between the PTFs obtained by the two approaches was shown for P_rem (Figure 3).

5. Conclusions

Highly weathered soils cover large areas in the tropics. The reactive minerals, i.e., clay minerals (kaolinite) and Al/Fe oxides (gibbsite, goethite, hematite), play a key role, together with organic matter, in the physico-chemical functioning of these soils, especially on P sorption. To overcome the widespread P deficiency in the agricultural soils of Sub-Saharan Africa and promote adequate soil P management, rapid and low-cost soil testing for P availability or P sorption capacity is needed. While numerous studies have been conducted to quantify the soil organic matter with infrared spectral methods (see [18]), research on the prediction of P sorption capacity or P availability in soils using this approach is still scarce. Although these methods are ineffective in predicting available P (P_resin), we showed that reliable spectroscopy-based analyses of a P sorption index (P_rem) can be obtained with both NIR and MIR spectrometry using mPLS. The development of pedotransfer functions (PTFs) based on carbon content, texture, and mineralogical properties of soils predicted with chemometric methods is also useful for predicting P_rem and through that in the understanding of the effects of the most important soil components controlling P sorption. Therefore, the P sorption capacity of the soil can be predicted based on the amounts of aluminum and iron oxides (gibbsite and Fe₂O_3cbd), which both increase P sorption, and the amount of sand, that counteract the effects of Fe/Al oxides. These soil components are fairly well predicted by IR-spectrometry, and a rapid and low-cost procedure for the estimation of P sorption capacity can be proposed. As farmers generally do not have access to soil testing in less developed countries (e.g., Madagascar), due to their cost and to the lack of routine laboratories, indices related to the P sorption potential of soils could be linked to cartographic data of the soils (i.e., mineralogy, C content) to improve fertilizers management. The hereby presented models represent encouraging results and foresee the need for similar studies on tropical soils in different environments to improve the method.