Remaining phosphorus estimated by pedotransfer function

Estimativa do fósforo remanescente por função de pedotransferência

DIVISÃO 3 - USO E MANEJO DO SOLO

3.1 - FERTILIDADE DO SOLO E NUTRIÇÃO DE PLANTAS

Remaining phosphorus estimated by pedotransfer function

Estimativa do fósforo remanescente por função de pedotransferência

Joice Cagliari^I; Maurício Roberto Veronez^II; Marcelo Eduardo Alves^III

^IProfessor of Centro de Ciências Exatas e Tecnologia, Universidade de Caxias do Sul – UCS. CEP 95070-560 Caxias do Sul (RS). E-mail: [e-mail]

^IIProfessor of Programa de Pós Graduação em Geologia, Universidade do Vale do Rio Sinos – Unisinos. CEP 93022-000 São Leopoldo (RS). E-mail: [e-mail]

^IIIProfessor of Departamento de Ciências Exatas, Escola Superior de Agricultura "Luiz de Queiroz" – ESALQ/USP. CEP 13418-900 Piracicaba (SP). E-mail: [e-mail]

SUMMARY

Although the determination of remaining phosphorus (Prem) is simple, accurate values could also be estimated with a pedotransfer function (PTF) aiming at the additional use of soil analysis data and/or Prem replacement by an even simpler determination. The purpose of this paper was to develop a pedotransfer function to estimate Prem values of soils of the State of São Paulo based on properties with easier or routine laboratory determination. A pedotransfer function was developed by artificial neural networks (ANN) from a database of Prem values, pH values measured in 1 mol L^-1 NaF solution (pH NaF) and soil chemical and physical properties of samples collected during soil classification activities carried out in the State of São Paulo by the Agronomic Institute of Campinas (IAC). Furthermore, a pedotransfer function was developed by regressing Prem values against the same predictor variables of the ANN-based PTF. Results showed that Prem values can be calculated more accurately with the ANN-based pedotransfer function with the input variables pH NaF values along with the sum of exchangeable bases (SB) and the exchangeable aluminum (Al³⁺) soil content. In addition, the accuracy of the Prem estimates by ANN-based PTF were more sensitive to increases in the experimental database size. Although the database used in this study was not comprehensive enough for the establishment of a definitive pedotrasnfer function for Prem estimation, results indicated the inclusion of Prem and pH NaF measurements among the soil testing evaluations as promising ind order to provide a greater database for the development of an ANN-based pedotransfer function for accurate Prem estimates from pH NaF, SB, and Al³⁺ values.

Index terms: Artificial neural networks, Modeling, Multiple regression analysis.

RESUMO

Embora de simples determinação, valores exatos de fósforo remanescente (Prem) poderiam ser estimados com uma função de pedotransferência visando ao aproveitamento adicional de resultados de análises de avaliação da fertilidade do solo ou sua substituição por uma determinação ainda mais simples. O objetivo do presente trabalho foi desenvolver uma função de pedotransferência para estimar o Prem em amostras de solos do Estado de São Paulo a partir de atributos de mais fácil ou rotineira determinação laboratorial. Uma função de pedotransferência foi desenvolvida por meio de redes neurais artificiais a partir de um conjunto de dados formado por valores de Prem, de pH determinado em solução de NaF 1 mol L^-1 (pH NaF) e de outros atributos de amostras coletadas durante as atividades de classificação de solo realizadas no Estado de São Paulo pelo Instituto Agronômico de Campinas. Adicionalmente, uma função de pedotransferência foi ajustada por meio de regressão linear múltipla, considerando-se o Prem como variável dependente das mesmas variáveis de entrada da função de pedotransferência desenvolvida via redes neurais artificiais. Os resultados indicaram que valores mais exatos de Prem podem ser estimados pela função de pedotransferência baseada em redes neurais artificiais tendo como variáveis de entrada valores de pH NaF, da soma de bases trocáveis (SB) e do teor de alumínio trocável (Al³⁺). Adicionalmente, observou-se que a exatidão das estimativas de Prem fornecidas pela rede neural artificial foi mais sensível ao aumento do número de dados experimentais utilizados para o desenvolvimento da função de pedotransferência. Apesar de o conjunto de dados utilizado não ser suficientemente abrangente para o estabelecimento de uma função de pedotransferência definitiva para estimativas de Prem, os resultados sugerem como promissora a inclusão de medidas de Prem e de pH NaF entre as análises de avaliação da fertilidade do solo com vistas à formação de um maior banco de dados, que permita o desenvolvimento de uma função de pedotransferência baseada em redes neurais artificiais para o cálculo de valores suficientemente exatos de Prem a partir de valores de pH NaF, SB e Al³⁺.

Termos de indexação: regressão linear múltipla, modelagem, redes neurais artificiais.

INTRODUCTION

The remaining phosphorus (Prem) refers to the P concentration that remains in solution after shaking a soil sample for a certain period with a solution with known initial P concentration. Since the soil adsorbs part or almost all added P, the Prem values are lower than the initial P concentration. This index was proposed by Bache & Williams (1971) to estimate the P adsorption capacity based on only one measurement and similarly to the adsorption isotherm method. The reference method for Prem measurement consists of shaking 2.5 g of air-dried fine earth (ADFE) for one hour with 25 mL of 0.01 mol L^-1 CaCl₂ containing 60 mg L^-1 P, filtering and/or centrifuging the soil suspension and determining the P concentration in the clear solution (Alvarez V. et al., 2000).

Although unlike anions such as nitrate that are adsorbed through electrostatic attraction, phosphate is mainly adsorbed by exchange with surface OH groups of minerals such as kaolinite, gibbisite, and goethite (Mott, 1981), it can be stated that soils with low Prem values tend to have higher levels of positive surface charges. In general, minerals such as gibbsite and goethite are more abundant in highly weathered soils; since these minerals have surface OH groups that can be changed with the phosphate anion and high values of point of zero charge, not only P adsorption is high in gibbsite and goethite-richer soils but also the number of positive surface charges, even under moderate acidity. Therefore, one can infer that soils with low Prem values can adsorb greater amounts of anions through both inner- and outer-sphere complexations.

The advantage of using Prem as anion-adsorption index is associated to its simpler and faster determination and the greater Prem dependency on the soil mineralogy than the clay content. The values of Prem and anion exchange capacity (AEC) in two soils with identical contents of clay-sized particles and same pH value measured in 0.01 mol L^-1 CaCl₂ can therefore differ considerably. Although the organic matter can delay P adsorption (Afif et al., 1995), in general, most tropical soils have low organic C contents and it can therefore be considered that the Prem values are essentially defined by the mineralogical compositions of the silt and clay fractions.

Phosphorus adsorption is related to the agronomic efficiency of P-bearing fertilizers (Novais & Smyth, 1999); for this reason, the amount of P fertilizer applied to a soil to ensure an adequate P nutrition of a crop must be greater in soils with higher gibbsite and goethite amounts; therefore, it is possible that the values of phosphate buffering capacity differ in two soils with the same clay contents. Likewise, tropical soils with low organic matter contents and identical clay contents can also differ in the acid buffering capacity due to mineralogical differences. The existence of soils with equal clay contents but different mineralogies makes Prem more adequate than the clay content as an auxiliary attribute for the interpretation of chemical soil analysis results in relation to the availability of some plant nutrients such as phosphorus, sulfur, and zinc, as well as for the calculation of the soil lime requirement as suggested by Alvarez V. et al. (2000).

In general, the soil P adsorption capacity is evaluated by the adsorption isotherm method; this approach is however rather time-consuming for routine chemical analyses in soil testing laboratories. Besides Prem, another possibility of evaluating the soil P adsorption consists of the soil pH values measured in 1 mol L^-1 NaF (pH NaF). This measurement was promising for the indirect evaluation of P adsorption in Australian soils (Singh & Gilkes, 1991; Gilkes & Hughes, 1994; Bolland et al., 1996). Afterwards, Alves & Lavorenti (2004) verified that higher pH NaF values are observed in soils with greater gibbsite contents, which partially explains the inverse correlation between Prem and pH NaF values. This consistent correlation and the simpler measurement could suggest the use of pH NaF instead of Prem as ancillary variable for the recommendation of P, S and lime requirements. However, the logarithmic scale makes the capacity of differentiating soils of pH NaF far lower than that of Prem, i.e., two soils having different Prem values can present similar pH NaF ones. Nevertheless, Alves & Lavorenti (2006) observed that the soil clay content could be replaced by pH NaF as predictive variable of Prem in multiple regression models.

Although the laboratory determination of Prem is quite simple, the possibility of estimating it with sufficient accuracy by other variables of routine or even simpler determination can make this determination quicker and cheaper. Such estimates can be obtained by so-called pedotransfer functions, which consist of equations or sets of equations that allow for estimating the value of a soil property from others with simpler and faster determination (Budiman et al., 2003). Usually, pedotransfer functions are developed from multiple linear regression models; however, more recently, these functions can be developed by using the artificial neural networks (ANN) approach, which are capable of identifying non-explicit relationships among the variables of a dataset (Tafner et al., 1996; Haykin, 2001; Braga, et al., 2007).

The purpose of this study was to develop pedotransfer functions by artificial neural networks and multiple linear regression for the calculation of remaining P values for soils in the State of São Paulo.

MATERIAL AND METHODS

The 89 soil samples used in this research were gotten from the collection formed along the soil classification activities carried out by the Agronomic Institute of Campinas (IAC) on the São Paulo State. These samples were collected from profiles and used as air-dried fine earth for Prem determinations according to the reference method proposed by Alvarez V. et al. (2000). Furthermore, pH measurements were conducted after shaking 1 g of soil for 1 h with 40 mL of 1 mol L^-1 NaF (Bolland et al., 1996). The other data characterized were the soil contents of clay-sized particles, of oxidazable C, and of exchangeable Al, Ca, Mg, and K. Additionally, the total acidity (H + Al), the pH values measured in water and in 1 mol L^-1 KCl and the soil contents of Fe, Al, and Si extractable with 9 mol L^-1 H₂SO₄ under boiling were also considered in the dataset used for the pedotransfer function development. Except for Prem and pH NaF, the values of the above-mentioned properties were provided by IAC; some of them had been cited in publications of Valladares et al. (1971), Oliveira et al. (1976), Oliveira et al. (1979), Oliveira & Prado (1984; 1987), Prado et al. (1999), Bertolani et al. (2000), Menk & Coelho (2000), Bognola et al. (2003), and Prado et al. (2003).

The artificial neural network-based pedotransfer function was developed with the option neural network toolbox of the MATLAB software. The applied network consisted of the perceptron multilayer whose topology was defined through successive tests. The dataset was normalized in the interval [0;1] and split in test subsets consisting of 50, 70, and 90 % of the total data. Several trainings and validations were carried out in order to find the best combination of input variables and the best network topology. Basically, the ANN was developed based on the so-called supervised training (Braga et al., 2007), a procedure in which the inputs and outputs are provided so as to fit the network parameters. The linear, the hyperbolic tangent sigmoid and the logistic sigmoid activation functions were tested, whereas the learning algorithms consisted of variations of backpropagation one (Levenberg-Marquartd, resilient backpropagation, and scaled conjugate gradient). The conclusion criterion used in the network test was the early stopping whereas the network performance was evaluated by the mean square error in the test stage and by the sum of the squared differences between measured and estimated Prem values by the pedotransfer function.

A second pedotransfer function was developed by multiple linear regression analysis with the software Statistical Analysis System – SAS 9.1 with the objective of establishing a functional relationship between Prem and the input variables that gave rise to the best artificial neural network. Similarly to the ANN, the regression equations were fitted with 50, 70 and 90 % of the total data and tested with the respective complimentary validation datasets.

The predictive capacities of the two pedotransfer functions were compared based on the fitting of the equation Prem_e = a + b Prem_m and by the calculation of the sum of the squared differences between the estimated (Prem_e) and the respective measured remaining phosphorus (Prem_m) values.

RESULTS AND DISCUSSION

The studied samples derived from different soil orders, mainly Latosols and Argisols (Embrapa, 2006) (Table 1). Most soils were clayey or very clayey (clay > 350 g kg^-1), strongly (4.3 < pH H₂O < 5.3) to moderately acidic (5.4 < pH H₂O < 6.5) (Embrapa, 2006) with differing weathering degrees (0.21 < Ki < 4.98). Although 73 % of the samples can be considered highly weathered (Ki < 2.0), only 17 % can be considered oxidic (Kr < 0.75) (Embrapa, 2006). The pH NaF values ranged from 8.3 to 10.5 and were inversely correlated with the Kr index (r = 0.51**), indicating an increasing trend of pH NaF when the samples become less kaolinitic (Alves & Lavorenti, 2004). Base saturation was low (V < 50 %) in about 75 % of the samples and the clay fraction activity low (T < 27 cmol_c kg^-1) (Embrapa, 2006) in almost all samples and the net surface charge negative (DpH < 0) (Mekaru & Uehara, 1972). The exchangeable Al³⁺ contents ranged from 0 to 5 cmol_c kg^-1 whereas the respective values of Al saturation and total acidity (H + Al) ranged from 0 to 98.5 % and from 0 to 15.4 cmol_c kg^-1. The sum of bases was directly correlated with the Ki index (r = 0.53**), in agreement with the loss of exchangeable bases that occurs as weathering advances.

The Prem values ranged from 0 to 47.3 mg L^-1 and although being inversely correlated with the soil clay content (r = -0.67**), were better correlated with pH NaF (r = -0.92**). This higher correlation can be ascribed to the inclusion in the pH NaF values of OH^- ions displaced from the mineral surfaces by the F^- ion (Perrott et al., 1976). Considering that the released OH^- surface groups are those that would be exchanged with phosphate ions in the adsorption process, higher pH NaF imply in lower Prem values.

The ANN-based pedotransfer function indicated that Prem values could be estimated from pH NaF values along with the correspondent soil contents of exchangeable Al³⁺ and of the sum of exchangeable bases (SB) (SB = Ca²⁺+ Mg²⁺ + K⁺). The best developed network used the logistic sigmoid model as activation function and the resilient backpropagation test algorithm with 21 cycles. The network topology was [3 14 1], corresponding to 3 neurons in the activation layer, 14 neurons in the intermediary and one neuron in the output layer.

Despite the high correlation of pH NaF with Prem, the latter was not correlated with Al³⁺ nor with SB values. On the other hand, Falcão & Silva (2004) observed that the soil maximum P adsorption capacity was directly correlated with the soil content of exchangeable Al and inversely correlated with base saturation in Amazonian alic soils. These correlations are possibly associated to the soil pH effect on P adsorption since soils rich in exchangeable Al are necessarily acidic, which favors P adsorption; likewise, pH values in soils with higher base sum and/or base saturation are normally higher, which, in turn, hampers P adsorption (Novais & Smyth, 1999). The fact that the variables SB and Al³⁺ are not correlated with Prem but nevertheless constitute, along with pH NaF, the best set of Prem predictive variables in the ANN-based pedotransfer function can be ascribed to the ANN capability of extracting non-explicit information from the dataset as well as solving non-linear problems.

The pedotransfer function developed by multiple regression analysis was fitted from the variables pH NaF, SB, and Al³⁺ considering the three subsets of adjustment (50, 70, and 90 % of total data) and validation (50, 30, and 10 % of total data). In all cases, the estimate of Al³⁺ coefficient was statistically zero (p > t > 5 %); for the adjustment subset with 90 % of data, only the pH NaF coefficient was statistically not zero (Table 2).

Although for both pedotransfer functions the accuracy of the Prem estimates increased with the augment of the dataset used for training or fitting (Figure 1), it was observed that this effect was greater for the ANN-based pedotransfer function. The summarized results (Table 3) show a reduction of almost 10 times in the sum of squared differences between the estimated and the respective Prem values of the validation subset when the network training subset consisted of 90 % instead of 50 % of the total data. For this same variation in the data subsets used to fit the multiple linear regression model, the sum of squared differences between estimated and measured Prem values was reduced by about six times.

The superior performance of artificial neural networks can be ascribed to their capacity of detecting relationships between input and output variables, which in most cases are either unknown or unnoticed. Another probable reason can be associated to the presence of distorted or incorrect information in the dataset. The artificial neural networks are less vulnerable to approximated data and/or to the presence of distorted data since they are able to manipulate approximated or even inaccurate information, a rather unusual feature in other mathematical models.

The use of Prem as determinant variable for soil stratification in classes of P, S, and Zn availability was presented by Alvarez V. et al. (2000). In this paper, the authors also suggested Prem as an estimator of the soil acidity buffering capacity for the calculation of lime requirements of cropped soils. This Prem use can, for instance, allow for the identification of different buffering capacities in soils with identical clay-sized particle contents. In this context, soils poor in organic matter and with low Prem values tend, due to their greater oxide contents, to require greater lime amounts for a same pH variation than soils with higher Prem values. The utility of the ANN-based pedotransfer function to estimate the acidity buffering factor Y proposed by Alvarez V. et al. (2000) ( = 4.002 0.125901 Prem + 0.001205 Prem² 0.00000362 Prem³) was tested considering the three subsets of training and validation data used in the development of the pedotransfer function. The results (Figure 2) reiterated the higher sensitivity of the ANN-based pedotransfer function to the increase in the test database in relation to the accuracy of the Prem estimates. The comparisons of the Y values calculated from measured with estimated Prem values revealed a progressive decrease in the sum of the squared differences (SSD) between the Y values calculated from measured and estimated Prem values as the ANN was developed from 50 % (SDD = 8.7) to 70 % (SDD = 2.8) and 90 % (SDD =0.9) of total input data in the training phase.

Despite the simple laboratory determination of Prem, the establishment of Prem estimates by a ANN-based pedotransfer function that are accurate enough for agricultural applications would allow for an additional use of both SB and Al³⁺ values routinely determined in the different Brazilian soil fertility laboratories. Although the number of samples used in this study did not allow for the development of a definitive pedotransfer function for Prem estimates, it is believed that the formation of a massive database containing Prem, pH NaF, SB, and Al³⁺ values is advisable for the posterior development of an ANN-based pedotransfer function which, once implemented as software, wil make an immediate calculation of remaining P values possible.

CONCLUSIONS

1. It was possible to estimate remaining P values with an artificial neural network-based pedotransfer function using soil pH values measured in 1 mol L^-1 NaF, soil contents of exchangeable Al, and the sum of soil contents of Ca, K and Mg as predictor variables.

2. The remaining P values estimated by the artificial neural network approach were more accurate than those obtained by multiple regression analysis.

ACKNOWLEDGEMENTS

The authors are indebted to the Brazilian Federal Agency for Support and Evaluation of Graduate Education -CAPES for the financial support and grateful to the researchers Mariana Cantoni, Cristiano Alberto Andrade, Ricardo Marques Coelho, and Márcio Koiti Chiba from the Agronomic Institute of Campinas - IAC for providing the soil samples used in this research and the respective analysis results.

LITERATURE CITED

Received for publication in December 2009 and approved in November 2010.

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Publication Dates

• Publication in this collection
  25 Apr 2011
• Date of issue
  Feb 2011

History

• Received
  Dec 2009
• Accepted
  Nov 2010