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Estimation of soil penetration resistance with standardized moisture using modeling by artificial neural networks
Catena 189 (2020) 104505
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Estimation of soil penetration resistance with standardized moisture using modeling by artificial neural networks
T
⁎
Mariele Monique Honorato Fernandes, Anderson Prates Coelho , Matheus Flavio da Silva, Rafael Scabello Bertonha, Renata Fernandes de Queiroz, Carlos Eduardo Angeli Furlani, Carolina Fernandes São Paulo State University (Unesp), School of Agricultural and Veterinarian Sciences, Via de Acesso Prof. Paulo Donato Castellane s/n, 14884-900 Jaboticabal, São Paulo, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Linear models Nonlinear models Models accuracy Soil moisture
One of the most used evaluations to monitor soil compaction is based on soil penetration resistance (SPR). However, since SPR is influenced by soil moisture, this evaluation performed in the field may often lead to incorrect interpretations. This study aimed to evaluate the accuracy of models in the estimation of soil penetration resistance with standardized moisture (SPRlab) based on soil penetration resistance measured in the field (SPRfield) and on soil moisture (U) and indicate the best soil layer and best model for that. Samplings were carried out in the years 2016 (72 points – 24 in each layer) and 2017 (270 points – 90 in each layer) in three soil layers (0.00–0.10 m, 0.10–0.20 m and 0.20–0.30 m). Samples collected in 2017 were used to calibrate the models and samples collected in 2016 were used to validate them. The models used were obtained by multiple linear and nonlinear regressions and artificial neural networks (ANNs). Models were calibrated with all sampled layers and stratified per layer. In the latter case, the samples were separated into two parts, one with the surface layer (0.00–0.10 m) and another with subsurface layers (0.10–0.20 m and 0.20–0.30 m). SPRlab can be estimated with high accuracy from SPRfield and U measured in the field. We recommend the use of ANN models (MLP or RBF) and soil samples collected from the 0.10–0.30 m layer for the monitoring of soil penetration resistance.
1. Introduction One of the most used evaluations to monitor soil compaction is based on soil penetration resistance (SPR). From the values of this attribute, critical limits can be defined for each crop and production system (Oliveira et al., 2016) in order to indicate a possible soil tillage and even the best type of operation for that. In addition, with the use geotechnologies, areas of specific management can be defined by thematic maps according to SPR (Oliveira Filho et al., 2015), reducing the time spent with the agricultural operation and, consequently, fuel consumption and use of labor, besides reducing CO2 emission from the operation. However, defining soil compaction by readings of soil penetration resistance taken in the field (SPRfield) often leads to incorrect
interpretations, because these readings are influenced by soil moisture (Moraes et al., 2013). The lower the moisture content in the soil, the higher its SPR (Oliveira et al., 2016) and vice versa, depending on the type of soil. Given the occurrence of spatial and temporal variability of soil moisture (U), the use of SPRfield values to define compacted areas is not recommended (Moraes et al., 2013; Valadão Júnior et al., 2014). Because of that, studies have been conducted to generate models and indicate methodologies to estimate SPR with standardized moisture (Vaz et al., 2011; Silva et al., 2016). To obtain soil samples in standardized moisture, the samples must be subjected to the same tension, generating soil samples with the same water tension. After that, readings and comparison of soil penetration resistance can be performed between samples. Nonetheless, the recommended methodologies are still costly, due
Abbreviations: SPR, soil penetration resistance; SPRlab, soil penetration resistance with standardized moisture; SPRfield, soil penetration resistance measured in the field; U, soil moisture (g g−1); ANN, artificial neural networks; MLP, artificial neural network multilayer-perceptron; RBF, artificial neural network radial-basisfunction; MLR, multiple linear regression; MNLR, multiple nonlinear regression; R2, coefficient of determination; RMSE, root-mean-square error; MBE, mean bias error; d, Willmott’s index of agreement ⁎ Corresponding author. E-mail addresses: [email protected] (A.P. Coelho), [email protected] (C.E.A. Furlani), [email protected] (C. Fernandes). https://doi.org/10.1016/j.catena.2020.104505 Received 13 February 2019; Received in revised form 30 January 2020; Accepted 30 January 2020 0341-8162/ © 2020 Elsevier B.V. All rights reserved.
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to the need for field samplings and laboratory analyses. In addition, in these studies there is no definition of layers which present the best accuracy in the estimation of soil penetration resistance determined in the laboratory (SPRlab) (Vaz et al., 2011; Silva et al., 2016). Such definition is essential because, due to the high variability of conditions to which the soil surface is subjected (Valadão Júnior et al., 2014; Colombi et al., 2018), this layer is expected to show greater variation of SPRfield and U readings than subsurface layers, which may negatively interfere with the accuracy of SPRlab estimation. By using models it is possible to estimate SPRlab as a function of SPRfield and U. However, defining the best model is essential because the estimation accuracy may be influenced. Among several models, artificial neural networks (ANNs) have gained attention because they are computer techniques which have mathematical models inspired in the neural structure of a human brain (Haykin, 1994). In this context, models generated by artificial neural networks (ANNs) have shown higher accuracy in the estimation of attributes, in comparison with linear and nonlinear regressions (Yilmaz and Kaynar, 2011; Kashi et al., 2014). This occurs because ANNs acquire knowledge by experience, being able to recognize patterns and make inferences (Haykin, 1994). The hypotheses tested in the present study are: artificial neural networks provide higher accuracy in SPRlab estimation than multiple linear and nonlinear regressions; samples from the surface soil layer negatively interfere with the accuracy of estimation of this attribute. Therefore, the aimed was to evaluate the accuracy of models in the estimation of soil penetration resistance with standardized moisture (SPRlab) as a function of soil penetration resistance measured in the field (SPRfield) and soil moisture (U) and indicate the best soil layer and best model for that.
water depth placed in a tray to 2/3 of the rings height for 24 h. After that, the rings were placed in a water tension table, the water tension being standardized at 0.01 MPa for all samples. SPRlab was determined in each sample, after applying the 0.01 MPa water tension, using a static electronic laboratory penetrometer. The static electronic laboratory penetrometer consists of a stylus that penetrate the sample at a speed of 1 cm per minute, generating 60 readings per minute. The volumetric rings are positioned so that the stylus penetrate the center of each undisturbed sample. Since the volumetric rings are 5 cm high, the penetrometer generates 300 readings per sample. For the calculation of SPRlab, an average of 180 readings is performed, excluding the first and last 60 readings of each sample. Samplings were carried out in the years 2016 and 2017. In 2016, 72 points were sampled, 24 points for each layer (0.00–0.10 m, 0.10–0.20 m and 0.20–0.30 m). In 2017, 270 points were sampled, 90 points for each layer. SPRfield was measured at each point and, simultaneously, beside the point where SPRfield was obtained, soil samples were collected to determine soil moisture and SPRlab. Soil penetration resistance measured in the laboratory (SPRlab), as a function of soil penetration resistance measured in the field (SPRfield) and soil moisture (U), was estimated using models generated by multiple linear regression (MLR), multiple nonlinear regression (MNLR) and radial-basis-function (RBF) and multilayer-perceptron (MLP) artificial neural networks (ANNs). Samples collected in 2017 (270) were used to calibrate the models, whereas those collected in 2016 (72) were used to validate them. Samples were collected at two years to evaluate the generalizability of the models, since the collection of samples in just one year can generate small data variability and generate models that are not generalist. In addition, due to the need for more data for the calibration phase, samples collected in 2017 were used to calibrate models and samples collected in 2016 to validate them. Models were calibrated with all sampled layers and stratified per layer. For the latter case (stratified per layer), samples were separated into two parts, one part with the surface layer (0.00–0.10 m) and the other with the subsurface layers (0.10–0.20 m and 0.20–0.30 m). Such procedure was carried out to check if there are better layers for soil compaction monitoring or if it does not depend on soil layer. Several crops such as soybean, corn, common bean, rice, peanuts and wheat have a high root depth up to 30 cm. Thus, the SPR can be monitored to a depth of 30 cm to monitor soil compaction and indicate possible agricultural managements. For this, in our study we stratified the 0.00–0.30 m layer into two layers: 0.00–0.10 m and 0.10–0.30 m. This was done because is difficult to study the properties of surface layer (0,00–0,10 m), due it is greatly affected by the soil texture and environment factors, which can lead to misinterpretations of the correct SPR values. Multiple linear and nonlinear regressions were calibrated and parameterized by the nonlinear GRG method (Abadie and Carpentier, 1969). ANNs were calibrated (trained) in the Intelligent Problem Solver mode of the program Statistica v.7. This mode allows several ANNs to be randomly trained, returning the quantity established previously based on those which showed lowest error. MLP ANNs were established with two hidden layers and number of neurons ranging from 8 to 40 in each layer, and the program returned 25 ANNs. The ANN with lowest root-mean-square error (RMSE) was selected for analysis. The training algorithm used was backpropagation, which is very robust for simulation of linear and nonlinear models (Haykin, 1994). The criterion to stop the calibration algorithm was the total number of cycles equal to 500 or mean square error lower than 1%. The activation function used was hyperbolic tangent (Eq. (1)).
2. Material and methods The data for the estimation of soil penetration resistance (SPR) determined in the laboratory (SPRlab) were obtained in an experimental area of the School of Agricultural and Veterinarian Sciences, São Paulo State University (Unesp), Brazil (21° 14′ 56″ S, 48° 16′ 52″ W, altitude of 572 m). According to Köppen’s classification, the climate of the region is Aw, subtropical, relatively dry in the winter, with summer rains, mean annual temperature of 22 °C and normal annual rainfall of 1425 mm (Alvares et al., 2013). The soil of the experimental area is classified as Eutrophic Red Oxisol (Soil Survey Staff, 2014). The soil of the experimental area had a particle-size distribution of 200 g kg−1 of sand, 290 g kg−1 of silt and 510 g kg−1 of clay (Claessen, 1997), being classified as clay (Soil Survey Staff, 2014). The geology of the area is located under the basalt of the Serra Geral Formation (IPT, 1981). The chemical analysis of the soil in the 0.00–0.20 m layer was: pH (CaCl2): 5.9, organic matter: 26 g dm−3, P: 43 mg dm−3, K: 4.7 mmolc dm−3, Ca: 44 mmolc dm−3, Mg: 23 mmolc dm−3, H + Al: 23 mmolc dm−3, sum of bases: 71.7 mmolc dm−3 e base saturation: 76%. The SPR measured in the field (SPRfield) was obtained by means of an automatic electronic penetrometer (PNT2000/M) attached to a fourwheeler (Suzuki Motors, LT-F160 QUAD-RUNNER model) and constructed according to the norm ASAE S313.3 (ASAE, 1999), in three soil layers (0.00–0.10 m, 0.10–0.20 m and 0.20–0.30 m). Soil samples for the determination of soil moisture (U) were collected beside the points where SPRfield was measured, and U was determined by the gravimetric method (Topp and Ferré, 2002). In this method, soil samples are first weighed and then taken in a forced circulation air oven at 105 °C to constant mass. After drying, they are weighed again and the moisture of each sample is calculated by the difference between the initial weight and the final weight divided by the final weight, the result being expressed in g water g soil−1. Close to the site where SPRfield and U values were obtained, an undisturbed sample was collected using volumetric rings (0.05 × 0.05 m), to determine SPRlab (Tormena et al., 1998). The volumetric rings for SPRlab determination were saturated by means of a
f(v) =
1 - e - av 1+e−av
where
f(v) = hyperbolic tangent activation function; 2
(1)
Catena 189 (2020) 104505
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a = estimate of the parameter which determines the hyperbolic tangent steepness; and, v = activation potential of the function.
Table 2 Number of neurons in each hidden layer of the models generated by artificial neural networks (ANNs) for each situation.
The RBF ANN has only one hidden layer, unlike the MLP, in which it is possible to choose the quantity of hidden layers. For RBF the number of neurons established for the hidden layer varied from 15 to 90 for the models with all layers and from 10 to 50 for the models stratified by layer. In each case, the ANN with lowest root-mean-square error (RMSE) was selected for analysis. The activation function for the RBF network is the radial basis function, defined by unsupervised techniques (Haykin, 1994). The statistical indices used to evaluate the accuracy of the SPRlab estimation models were the coefficient of determination (R2), rootmean-square error (RMSE) (Eq. (2)), mean bias error (MBE) (Eq. (3)) and Willmott’s index of agreement (d) (Willmott, 1981) (Eq. (4)). Outliers were removed according to the methodology proposed by Belsley et al. (1980).
i=1
(2)
N
∑ (Yobs i − Yesti) MBE =
i=1
(3)
N N
∑ (Yobs i − Yesti)2 d= 1−
i=1 N
∑ (|Yesti − Y¯| + |Yobs i − Y¯|)2 i=1
Number of neurons in each hidden layer
RBF
0.00–0.30 0.00–0.10 0.10–0.30
40 50 54
MLP
0.00–0.30 0.00–0.10 0.10–0.30
40–28 40–25 40–29
models as a function of SPRfield and U (Table 3). Firstly, the models were applied to all data of the three layers evaluated in the field (0.00–0.10; 0.10–0.20 and 0.20–0.30 m). Then, the samples of the 0.00–0.10 m layer were removed from the data set and the models were calibrated again. This procedure was carried out with the expectation that samples from the 0.00–0.10 m layer had high variability, which could interfere with the accuracy of the models. This was confirmed for the data observed in the calibration and validation, since the data of the 0.00–0.10 m layer showed higher standard error of the mean compared to the other layers (Table 3). According to the data of the mean, the values estimated by the models were very close to the observed ones, for the phases of both calibration and validation, except the data of validation of RBF ANN in the first layer, where the difference for the mean was higher than 0.3 MPa. In relation to maximum and minimum values, in an overall analysis between models for layers and phases (calibration and validation), the ANNs (MLP and RBF) had closer estimates than what was observed in the laboratory. The regressions (MLR and MNLR), in general, underestimated the maximum values observed, except for the MLR in the 0.10–0.30 m layer for the validation phase, and overestimated the minimum values, except for MNLR in the 0.00–0.30 m layer for the calibration phase, indicating lower amplitude in the estimation of SPRlab compared to the ANNs. The four models, applied to the data set evaluated in the 0.00–0.30 m layer, showed similar statistical indices of performance in the prediction accuracy between the calibration and validation phases, i.e., they showed generalization capacity and can be applied to other data sets (Fig. 1). However, when the models are compared, it can be observed that ANNs (RBF and MLP) showed higher accuracy than MLR and MNLR. Both the coefficient of determination (R2) and the error (RMSE) were better for the prediction by ANNs. In the overall mean of the calibration and validation phases of the models, the precision of ANNs (R2) was 86% higher and the error (RMSE) was 22% lower than those of the two multiple regressions. The accuracy between the ANNs (RBF and MLP) was similar. By using only the samples from the 0.00–0.10 m layer and applying the models, it can be noted that MLR and MNLR showed low accuracy in the prediction (Fig. 2), with lower precision and higher error compared to the situation in which the samples of all layers were used. In
N
N
Layer (m)
RBF – radial basis function; MLP – multilayer perceptron; Values for the RBF and MLP ANN models indicate number of neurons in the hidden layers.
∑ (Yobs i − Yesti)2 RMSE =
ANN model
(4)
where
N = total number of data in each model; Yobs i = observed values of Y; and, Yesti = estimated values of Y. 3. Results Four models were applied to assess the prediction accuracy in the estimation of values of soil penetration resistance (SPR) determined in the laboratory (SPRlab), with standardized moisture of the sample, based on the values of SPR determined in the field (SPRfield), with variable moisture (U) according to the local conditions. Multiple linear (MLR) and nonlinear (MNLR) regression models were calibrated for the data in different layers and applied to assess the accuracy in the validation data (Table 1). Artificial neural networks (ANNs) were applied in the estimation but, since there is definition of equations, the complexity of RBF and MLP ANNs was presented, indicating the number of neurons in the hidden layers for each situation (Table 2). Descriptive statistics was used in the data of soil penetration resistance determined in the laboratory (SPRlab) and estimated by the
Table 1 Equations calibrated for multiple linear and nonlinear regression models as a function of layers and applied to the validation data. Model
Layer (m)
Regression
MLR
0.00–0.30 0.00–0.10 0.10–0.30
SPRlab = 0.059 * SPRfield − 11.549 * U + 5.701 SPRlab = 0.518 * SPRfield − 5.807 * U + 3.971 SPRlab = 0.006 * SPRfield − 18.830 * U + 7.783
MNLR
0.00–0.30 0.00–0.10 0.10–0.30
SPRlab = 0.0008 * SPRfield2 − 166.369 * U2 + 0.042 * SPRfield + 77.985 * U − 6.274 SPRlab = -0.0012 * SPRfield2 − 147.908 * U2 + 0.237 * SPRfield + 73.711 * U − 6.584 SPRlab = 0.0124 * SPRfield2 − 77.643 * U2 − 0.039 * SPRfield + 23.053 * U + 2.175
MLR – multiple linear regression; MNLR – multiple nonlinear regression; SPRlab – soil penetration resistance measured in the laboratory (MPa); SPRfield – soil penetration resistance measured in the field (MPa); U – field soil moisture (g g−1). 3
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Table 3 Descriptive statistics for soil penetration resistance (SPR), measured in the laboratory (Observed), and estimated by the models for calibration and validation phases as a function of the layers used. Model
Calibration data 0.00–0.30 m
Validation data 0.00–0.10 m
0.10–0.30 m
0.00–0.30 m
0.00–0.10 m
0.10–0.30 m
2.74 2.77 2.76 2.75 2.72
Observed MLR MNLR RBF ANN MLP ANN
————————Mean – MPa———————— ————————Mean – MPa———————— 2.67 ± 0.03 2.46 ± 0.05 2.81 ± 0.03 2.79 ± 0.06 2.67 ± 0.02 2.46 ± 0.02 2.81 ± 0.02 2.68 ± 0.03 2.67 ± 0.02 2.46 ± 0.03 2.81 ± 0.02 2.66 ± 0.03 2.67 ± 0.02 2.47 ± 0.05 2.81 ± 0.03 2.70 ± 0.03 2.67 ± 0.02 2.47 ± 0.05 2.81 ± 0.03 2.72 ± 0.05
2.47 2.46 2.44 2.11 2.39
Observed MLR MNLR RBF ANN MLP ANN
————————Maximum – MPa—————— ————————Maximum – MPa———————— 4.46 3.29 4.46 3.99 3.24 2.78 3.33 3.56 3.07 2.71 3.27 3.02 3.73 3.29 4.24 3.26 3.85 3.23 4.16 4.28
3.24 2.71 2.69 3.18 3.13
3.99 4.20 3.72 3.59 4.21
Observed MLR MNLR RBF ANN MLP ANN
————————Minimum – MPa——————— ————————— Minimum – MPa———————— 1.37 1.37 1.86 1.80 1.90 2.14 2.04 2.12 1.36 1.68 1.95 1.91 1.65 1.54 1.85 2.17 1.82 1.59 1.93 2.09
1.81 2.23 2.12 0.93 1.15
2.01 2.17 2.11 2.13 1.87
± ± ± ± ±
0.08 0.03 0.04 0.12 0.09
± ± ± ± ±
0.06 0.05 0.05 0.06 0.07
MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. Mean values are followed by the standard error of the mean.
layers, and for soil tillage, providing environment for the development of the root system of crops. In addition, mapping of SPR may indicate areas of specific management (Oliveira Filho et al., 2015), reducing the time spent with the agricultural operation and consequently fuel consumption and use of labor, besides reducing CO2 emission from the agricultural operation. However, the definition of soil compaction by readings of soil penetration resistance taken in the field often leads to error, because these readings are influenced by soil moisture (Moraes et al., 2013). Because of that, studies have been conducted to generate models to estimate SPR with standardized moisture (Vaz et al., 2011; Silva et al., 2016). The spatial variability of SPR is influenced by soil moisture, and the higher the moisture content the lower the spatial dependence (Souza et al., 2006). Besides the moisture content, SPR is also influenced by soil texture, organic matter content and mineralogy (Vaz et al., 2013). Therefore, the models for SPR estimation with standardized moisture should be generated for each type of soil and, preferably, calibrated locally. Vaz et al. (2011), evaluating the accuracy of models in the prediction of SPRlab as a function of moisture, observed that model calibration for each type of soil and selection of the ideal model are fundamental for the estimation accuracy, since the precision may double with the correct choice. This can be observed in the present study, in which choosing the ANN model leads to higher accuracy of estimation compared to the others. Silva et al. (2016) proposed to estimate SPRlab based on soil moisture and density using nonlinear modeling. The precision observed by these authors (R2 = 0.68) was close to that obtained in the present study; however, operationally, the applied methodology is more expensive and time-consuming than that proposed here. In the methodology proposed by Silva et al. (2016), along the entire monitoring it is necessary to define soil density in the laboratory, which requires the collection of undisturbed soil samples. In the present study, after the calibration and validation of the models, SPRlab monitored is carried out by measurements taken in the field (SPRfield and moisture, simultaneously), using devices and sensors, such as the automatic electronic penetrometer (PNT2000/M) attached to a four-wheeler, which is very practical. Although there are studies to model SPRlab based on soil moisture (Vaz et al., 2011; Silva et al., 2016), none of them conducted an analysis of the layers which showed the best estimate. This becomes necessary
the calibration, the generated models were significant but there was no significance when the models were applied to another data set, since the statistical coefficients of the validation phase were very different from those of the calibration, indicating that models generated by MLR and MNLR cannot be applied to estimate SPRlab using data of the surface layer (0.00–0.10 m). For the ANNs, the calibration phase showed high accuracy, much higher than that observed using all samples. However, when the generated models were applied to the data of validation, the accuracy was greatly reduced, with statistical coefficients lower than those observed in the model with all samples. This indicates that all models generated for the surface layer (0.00–0.10 m) do not have generalization capacity, which can be explained by the greater variation of SPR in this layer, compared to the other data sets, as evidenced by the standard error of the mean for this layer (Table 3). For the models generated with data of the subsurface layers (0.10–0.30 m), it was observed that in the calibration phase the ANNs showed higher precision and lower error than the regressions (Fig. 3). Also for this phase, all models showed higher accuracy than that obtained with the data using all layers (Fig. 1) and the ANNs showed higher accuracy than MLR and MNLR. It can be noted that the R2 values of MLR and MNLR increased from the calibration phase to the validation phase, a fact not observed in the ANN models, in which the statistical indices of performance were similar between the phases. It is desirable that the values of the indices be similar when the model is applied to other data sets, since large differences may indicate low generalization by the model, especially when the values reduce the accuracy (Sargent, 2013). The difference in values between the calibration and validation phases did not reduce the accuracy of the models. However, the increased accuracy of the MLR and MNLR models may indicate low generalizability by these models. Based on the statistical indices of performance of the models, it is possible to observe that the estimation accuracy increased when the samples from the 0.00–0.10 m layer were removed for calibration and subsequent validation. 4. Discussion Mapping the soil penetration resistance (SPR) of agricultural areas is fundamental for the recommendation of subsoiling to break compacted 4
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Calibration
Validation
MLR
MNLR
RBF ANN
MLP ANN
Fig. 1. Performance graphs of the estimation of soil penetration resistance (SPR) for the models in the calibration and validation phases using all layers (0.00–0.30 m). MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. R2 – coefficient of determination; d – Willmott’s index of agreement; RMSE – root-mean-square error; MBE – mean bias error; ns – not significant; * significant at 0.05 probability level; ** significant at 0.01 probability level.
readings is expected in this layer, as SPRfield is influenced by soil moisture and the loss of water in agricultural areas is not uniform (Colombi et al., 2018). Additionally, the variation may occur according to the plant material and amount of straw present on soil surface, interfering with SPRfield readings in surface layers (Valadão Júnior et al., 2014). Although the soil surface layer (0.00–0.10 m) concentrates a large
because a certain layer may not be technically adequate for the prediction, a fact observed in the present study, in which the accuracy increased when the samples from the surface layer (0.00–0.10 m) were removed for calibration of the models. Therefore, samples from the 0.10–0.30 m layer are recommended for SPRlab monitoring. Since most of the root system of crops and spontaneous vegetation in agricultural areas is concentrated in the surface layer, a large variation in SPRfield 5
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Calibration
Validation
MLR
MNLR
RBF ANN
MLP ANN
Fig. 2. Performance graphs of the estimation of soil penetration resistance (SPR) for the models in the calibration and validation phases using the 0.00–0.10 m layer. MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. R2 – coefficient of determination; d – Willmott’s index of agreement; RMSE – root-mean-square error; MBE – mean bias error; ns – not significant; * significant at 0.05 probability level; ** significant at 0.01 probability level.
to misunderstandings (Bonnin et al., 2010; Pias et al., 2018). Thus, as the roots of the crops develop to deeper layers (30–40 cm), the monitoring of SPR in subsurface layers (0.10–0.30 m) is an alternative in monitoring soil compaction and indicating of possible agricultural managements (Alesso et al., 2019). In the present study, the definition of models was carried out under specific conditions, such as the soil type used, equipment used for
amount of roots, most crops such as corn, soybean, common bean, rice, sugarcane and wheat have effective root depths of 30 to 40 cm deep in the soil (Allen et al., 1998). Effective root depth represents the soil layer where 80% of the total plant roots are concentrated. Due to factors such as soil moisture, temperature, radiation and machine traffic, the surface layer presents high variability, which makes it difficult to monitor soil compaction through SPR readings on the surface layer, which may lead 6
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Calibration
Validation
MLR
MNLR
RBF ANN
MLP ANN
Fig. 3. Performance graphs of the estimation of soil penetration resistance (SPR) for the models in the calibration and validation phases using the 0.10–0.30 m layer. MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. R2 – coefficient of determination; d – Willmott’s index of agreement; RMSE – root-mean-square error; MBE – mean bias error; ns – not significant; * significant at 0.05 probability level; ** significant at 0.01 probability level.
and the type of soil used, the models can be recommended and present application in any locations. This can be done both to indicate the best soil layers for the highest accuracy, as well as to recommend the models for applications elsewhere. Thus, we recommend using the methodology proposed in the present study for each area and then applying the generated models to monitor the spatial variation of SPRlab, in possible zones of specific management, with the devices used in the calibration of the models. However, as SPR is influenced by soil texture (Moraes et al., 2013), in
SPRlab and SPRfield readings, model types and soil layers used. If there is a change in any characteristic of the methodology, such as sampled soil layers, devices used to evaluate soil moisture and SPRfield, device to measure SPRlab etc., the accuracy of the results should be checked, possibly requiring calibration of new models. The studies of Hernanz et al. (2000); Valadão Júnior et al. (2014) demonstrate that, in which the size of the base of the cone used to measure SPRfield significantly influences the values; smaller bases increase SPRfield values. However, under conditions similar to the present study regarding the equipment 7
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Declaration of Competing Interest
areas where clay content is similar to that of the soil evaluated in the present study, one can use the models calibrated here for SPRlab prediction using SPRfield and U measures. In relation to the models, it can be observed that ANNs showed higher accuracy than MLR and MNLR, and no relevant differences were observed between the types of ANN (RBF or MLP). For having the capacity to recognize patterns within data sets, studies have demonstrated that ANNs have higher prediction accuracy than other models and may show a 40% higher precision (Yilmaz and Kaynar, 2011; Kashi et al., 2014). According to statistical indices and depending on generalizability, some models are more suitable for certain data sets than others. So, we found in the present study that the ANNs models presented higher precision (R2) and lower error (RMSE) than MLR and MNLR models. Thus, ANNs are more accurate models and should be indicated for the estimation of SPR. In addition, another key step in choosing the best models is the similarity of accuracy between the calibration and validation phases. Models that present very different statistical indices values between the calibration and validation phases tend to be less generalist and more likely to error (Sargent, 2013). Usually, MLP ANNs have high estimation accuracy, being superior to RBF ANNs (Paschalidou et al., 2011; Kashi et al., 2014). Due to their architecture with more than one hidden layer, these models are more generalist and their application in other data sets is more recommended compared to RBF ANNs (Haykin, 1994). Nonetheless, this fact was not observed in the present study, and both models are recommended for SPRlab estimation. Depending on the data set and objective of the study, RBF or MLP ANNs can be indicated. When the data have large variability of error, RBF ANNs are more recommended than MLP ANNs because they have activation functions that reduce the amplitude of errors (Xie et al., 2011). However, according to the authors, if the problem is more linearly separable, MLP ANNs are recommended because of their more complex structure, capable of better recognizing data patterns. For the present study, MLP and RBF ANNs had similar accuracies and were recommended for SPRlab estimation. In addition, samples from the 0.10–0.30 m layer are recommended for the calibration of the models and subsequent application to estimate SPRlab. SPRfield determination with variable moisture limits the comparison of SPR values. In the same area of the present study, Chioderoli (2013) evaluated SPRfield and soil moisture (U) before the sowing of corn (SPRfield = 2.70 MPa and U = 0.27 g g−1) and after its harvest (SPRfield = 2.08 MPa and U = 0.37 g g−1). This author observed that SPRfield values were higher before sowing than after harvest, which may indicate a possible beneficial effect of corn for soil decompaction. However, when the model generated by MLP ANN for soil samples collected in the 0.10–0.30 m layer, proposed in the present study, was applied using the SPRfield and U values presented by Chioderoli (2013), it could be observed that, with standardized soil moisture, SPRlab was similar for both periods, 2.73 MPa before corn sowing and 2.77 MPa after its harvest. Therefore, it is fundamental to obtain SPR with standardized moisture in order to allow for the comparison between SPR values determined along the production cycle of several crops, in order to assess the influence of the various management systems on soil physical quality.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors thank the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for granting the scholarships to the first, third and fifth authors, and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for granting the scholarship to the second author. References Abadie, J., Carpentier, J., 1969. Generalization of the wolf reduced gradient method to the case of nonlinear constraints. In: Optimization. R. Fletcher 9ed, Academic Press, New York, pp. 37–47. Alesso, C.A., Masola, M.J., Carrizo, M.E., Cipriotti, P.A., Imhoff, S.D., 2019. Spatial variability of short-term effect of tillage on soil penetration resistance. Arch. Agron. Soil Sci. 65, 822–832. https://doi.org/10.1080/03650340.2018.1532076. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. Fao, Rome 300 (9), D05109. Alvares, C.A., Stape, J.L., Sentelhas, P.C., de Moraes, G., Leonardo, J., Sparovek, G., 2013. Köppen's climate classification map for Brazil. Meteorol. Z. 22, 711–728. https://doi. org/10.1127/0941-2948/2013/0507. American society of agricultural engineers (ASAE), 1999. Agricultural Machinery Management. EP 496.2. In: ASAE standards: Standards engineering practices data. American Society of Agricultural Engineers, St. Joseph, pp. 353–358. Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression diagnostics: Identifying influential data and sources of collinearity, 1st ed. John Wiley & Sons, New York, pp. 100p. Bonnin, J.J., Mirás-Avalos, J.M., Lanças, K.P., González, A.P., Vieira, S.R., 2010. Spatial variability of soil penetration resistance influenced by season of sampling. Bragantia 69, 163–173. https://doi.org/10.1590/S0006-87052010000500017. Chioderoli, C.A., 2013. Intercropping of Urochloas with maize in no-tillage system cultivated before summer soybean. Universidade Estadual Paulista – Faculdade de Ciências Agrárias e Veterinárias de Jaboticabal, pp. 200 Doctoral thesis. Claessen org., M.E.C., 1997. Manual de métodos de análise de solo, 2nd ed. Centro Nacional de Pesquisa de Solos, Rio de Janeiro. Colombi, T., Torres, L.C., Walter, A., Keller, T., 2018. Feedbacks between soil penetration resistance, root architecture and water uptake limit water accessibility and crop growth–A vicious circle. Sci. Total Environ. 626, 1026–1035. https://doi.org/10. 1016/j.scitotenv.2018.01.129. Haykin, S., 1994. Neural networks: a comprehensive foundation, 2nd ed. Prentice-Hall, Englewood Cliffs, NJ. Hernanz, J.L., Peixoto, H., Cerisola, C., Sánchez-Girón, V., 2000. An empirical model to predict soil bulk density profiles in field conditions using penetration resistance, moisture contente and soil depth. J. Terramechanics. 37, 167–184. https://doi.org/ 10.1016/S0022-4898(99)00020-8. IPT – Instituto de Pesquisas Tecnológicas do Estado de São Paulo. 1981. Mapa geomorfológico do Estado de São Paulo 1981. São Paulo, pp. 94. Kashi, H., Emamgholizadeh, S., Ghorbani, H., 2014. Estimation of soil infiltration and cation exchange capacity based on multiple regression, ANN (RBF, MLP), and ANFIS models. Commun. Soil Sc. Plant An. 45, 1195–1213. https://doi.org/10.1080/ 00103624.2013.874029. Moraes, M.T.D., Debiasi, H., Franchini, J.C., Silva, V.R.D., 2013. Soil penetration resistance in a rhodic eutrudox affected by machinery traffic and soil water content. Eng. Agric. 33, 748–757. https://doi.org/10.1590/S0100-69162013000400014. Oliveira, P.D.D., Sato, M.K., Lima, H.V.D., Rodrigues, S., Silva, A.P.D., 2016. Critical limits of the degree of compactness and soil penetration resistance for the soybean crop in N Brazil. J. Plant Nutr. Soil Sc. 179, 78–87. https://doi.org/10.1002/jpln. 201400315. Oliveira Filho, F.X., Miranda, N.D.O., Medeiros, J.F., Silva, P., Mesquita, F.O., Costa, T.K., 2015. Management zones for subsoiling of a sugarcane field. Rev. Bras. Eng. Agric. Amb. 19, 186–193. https://doi.org/10.1590/1807-1929/agriambi.v19n2p186-193. Paschalidou, A.K., Karakitsios, S., Kleanthous, S., Kassomenos, P.A., 2011. Forecasting hourly PM 10 concentration in Cyprus through artificial neural networks and multiple regression models: implications to local environmental management. Environ. Sci. Pollut. R. 18, 316–327. https://doi.org/10.1007/s11356-010-0375-2. Pias, O.H.D.C., Cherubin, M.R., Basso, C.J., Santi, A.L., Molin, J.P., Bayer, C., 2018. Soil penetration resistance mapping quality: effect of the number of subsamples. Acta Scient. Agro. 40, e34989. https://doi.org/10.4025/actasciagron.v40i1.34989. Sargent, R.G., 2013. Verification and validation of simulation models. J. Simul. 7, 12–24. Silva, W.M.D., Bianchini, A., Cunha, C.A.D., 2016. Modeling and correction of soil penetration resistance for variations in soil moisture and soil bulk density. Eng. Agric. 36, 449–459. https://doi.org/10.1590/1809-4430-Eng.Agric.v36n3p449-459/2016. Soil Survey Staff, 2014. Soil taxonomy, 12th ed. USDANRCS, Washington DC, USA, Washington DC. Souza, Z.M.D., Campos, M.C.C., Cavalcante, Í.H.L., Marques Júnior, J., Cesarin, L.G.,
5. Conclusions Soil penetration resistance measured in the laboratory can be estimated with high accuracy based on soil penetration resistance and soil moisture measured in the field. Models with data from the surface layer (0.00–0.10 m) are not recommended to estimate soil penetration resistance measured in the laboratory. Artificial neural networks have higher estimation accuracy than multiple linear and nonlinear regressions. We recommend the use of models generated by artificial neural networks (MLP or RBF) and samples from the 0.10–0.30 m layer for the monitoring of soil penetration resistance. 8
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penetration resistance for varying soil water content. Geoderma 166, 92–101. https://doi.org/10.1016/j.geoderma.2011.07.016. Vaz, C.M., Manieri, J.M., Maria, I.C., 2013. Scaling the dependency of soil penetration resistance on water content and bulk density of different soils. Soil Sci. Soc. Am. J. 77, 1488–1495. https://doi.org/10.2136/sssaj2013.01.0016. Willmott, C.J., 1981. On the validation of models. Phys. Geogr. 2, 184–194. Xie, T., Yu, H., Wilamowski, B., 2011. Comparison between traditional neural networks and radial basis function networks. In: IEEE International Symposium on Industrial Electronics (ISIE). IEEE, pp. 1194–1199. Yilmaz, I., Kaynar, O., 2011. Multiple regression, ANN (RBF, MLP) and ANFIS models for prediction of swell potential of clayey soils. Expert Syst. Appl. 38, 5958–5966. https://doi.org/10.1016/j.eswa.2010.11.027.
Souza, S.R.D., 2006. Spatial variability of soil penetration resistance and soil moisture at different periods of sampling under sugarcane crop. Cienc. Rural. 36, 128–134. https://doi.org/10.1590/S0103-84782006000100019. Topp, G.C., Ferré, P.A., 2002. The soil solution phase. In: Dane, J.H., Topp, G.C. (Eds.), Methods of Soil Analysis, Part 4, Physical Methods. Soil Science Society of America Inc, Madison, pp. 417–1074. Tormena, C.A., Silva, A.P., Libardi, P.L., 1998. Characterization of the least limiting water range of an oxisol under no-tillage. Rev. Bras. Cienc. Solo. 22, 573–581. https://doi. org/10.1590/S0100-06831998000400002. Valadão Junior, D.D., Biachini, A., Valadão, F.C.A., Rosa, R.P., 2014. Penetration resistance according to penetration rate, cone base size and different soil conditions. Bragantia 73, 171–177. https://doi.org/10.1590/brag.2014.013. Vaz, C.M., Manieri, J.M., Maria, I.C., Tuller, M., 2011. Modeling and correction of soil
9
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Estimation of soil penetration resistance with standardized moisture using modeling by artificial neural networks
T
⁎
Mariele Monique Honorato Fernandes, Anderson Prates Coelho , Matheus Flavio da Silva, Rafael Scabello Bertonha, Renata Fernandes de Queiroz, Carlos Eduardo Angeli Furlani, Carolina Fernandes São Paulo State University (Unesp), School of Agricultural and Veterinarian Sciences, Via de Acesso Prof. Paulo Donato Castellane s/n, 14884-900 Jaboticabal, São Paulo, Brazil
A R T I C LE I N FO
A B S T R A C T
Keywords: Linear models Nonlinear models Models accuracy Soil moisture
One of the most used evaluations to monitor soil compaction is based on soil penetration resistance (SPR). However, since SPR is influenced by soil moisture, this evaluation performed in the field may often lead to incorrect interpretations. This study aimed to evaluate the accuracy of models in the estimation of soil penetration resistance with standardized moisture (SPRlab) based on soil penetration resistance measured in the field (SPRfield) and on soil moisture (U) and indicate the best soil layer and best model for that. Samplings were carried out in the years 2016 (72 points – 24 in each layer) and 2017 (270 points – 90 in each layer) in three soil layers (0.00–0.10 m, 0.10–0.20 m and 0.20–0.30 m). Samples collected in 2017 were used to calibrate the models and samples collected in 2016 were used to validate them. The models used were obtained by multiple linear and nonlinear regressions and artificial neural networks (ANNs). Models were calibrated with all sampled layers and stratified per layer. In the latter case, the samples were separated into two parts, one with the surface layer (0.00–0.10 m) and another with subsurface layers (0.10–0.20 m and 0.20–0.30 m). SPRlab can be estimated with high accuracy from SPRfield and U measured in the field. We recommend the use of ANN models (MLP or RBF) and soil samples collected from the 0.10–0.30 m layer for the monitoring of soil penetration resistance.
1. Introduction One of the most used evaluations to monitor soil compaction is based on soil penetration resistance (SPR). From the values of this attribute, critical limits can be defined for each crop and production system (Oliveira et al., 2016) in order to indicate a possible soil tillage and even the best type of operation for that. In addition, with the use geotechnologies, areas of specific management can be defined by thematic maps according to SPR (Oliveira Filho et al., 2015), reducing the time spent with the agricultural operation and, consequently, fuel consumption and use of labor, besides reducing CO2 emission from the operation. However, defining soil compaction by readings of soil penetration resistance taken in the field (SPRfield) often leads to incorrect
interpretations, because these readings are influenced by soil moisture (Moraes et al., 2013). The lower the moisture content in the soil, the higher its SPR (Oliveira et al., 2016) and vice versa, depending on the type of soil. Given the occurrence of spatial and temporal variability of soil moisture (U), the use of SPRfield values to define compacted areas is not recommended (Moraes et al., 2013; Valadão Júnior et al., 2014). Because of that, studies have been conducted to generate models and indicate methodologies to estimate SPR with standardized moisture (Vaz et al., 2011; Silva et al., 2016). To obtain soil samples in standardized moisture, the samples must be subjected to the same tension, generating soil samples with the same water tension. After that, readings and comparison of soil penetration resistance can be performed between samples. Nonetheless, the recommended methodologies are still costly, due
Abbreviations: SPR, soil penetration resistance; SPRlab, soil penetration resistance with standardized moisture; SPRfield, soil penetration resistance measured in the field; U, soil moisture (g g−1); ANN, artificial neural networks; MLP, artificial neural network multilayer-perceptron; RBF, artificial neural network radial-basisfunction; MLR, multiple linear regression; MNLR, multiple nonlinear regression; R2, coefficient of determination; RMSE, root-mean-square error; MBE, mean bias error; d, Willmott’s index of agreement ⁎ Corresponding author. E-mail addresses: [email protected] (A.P. Coelho), [email protected] (C.E.A. Furlani), [email protected] (C. Fernandes). https://doi.org/10.1016/j.catena.2020.104505 Received 13 February 2019; Received in revised form 30 January 2020; Accepted 30 January 2020 0341-8162/ © 2020 Elsevier B.V. All rights reserved.
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to the need for field samplings and laboratory analyses. In addition, in these studies there is no definition of layers which present the best accuracy in the estimation of soil penetration resistance determined in the laboratory (SPRlab) (Vaz et al., 2011; Silva et al., 2016). Such definition is essential because, due to the high variability of conditions to which the soil surface is subjected (Valadão Júnior et al., 2014; Colombi et al., 2018), this layer is expected to show greater variation of SPRfield and U readings than subsurface layers, which may negatively interfere with the accuracy of SPRlab estimation. By using models it is possible to estimate SPRlab as a function of SPRfield and U. However, defining the best model is essential because the estimation accuracy may be influenced. Among several models, artificial neural networks (ANNs) have gained attention because they are computer techniques which have mathematical models inspired in the neural structure of a human brain (Haykin, 1994). In this context, models generated by artificial neural networks (ANNs) have shown higher accuracy in the estimation of attributes, in comparison with linear and nonlinear regressions (Yilmaz and Kaynar, 2011; Kashi et al., 2014). This occurs because ANNs acquire knowledge by experience, being able to recognize patterns and make inferences (Haykin, 1994). The hypotheses tested in the present study are: artificial neural networks provide higher accuracy in SPRlab estimation than multiple linear and nonlinear regressions; samples from the surface soil layer negatively interfere with the accuracy of estimation of this attribute. Therefore, the aimed was to evaluate the accuracy of models in the estimation of soil penetration resistance with standardized moisture (SPRlab) as a function of soil penetration resistance measured in the field (SPRfield) and soil moisture (U) and indicate the best soil layer and best model for that.
water depth placed in a tray to 2/3 of the rings height for 24 h. After that, the rings were placed in a water tension table, the water tension being standardized at 0.01 MPa for all samples. SPRlab was determined in each sample, after applying the 0.01 MPa water tension, using a static electronic laboratory penetrometer. The static electronic laboratory penetrometer consists of a stylus that penetrate the sample at a speed of 1 cm per minute, generating 60 readings per minute. The volumetric rings are positioned so that the stylus penetrate the center of each undisturbed sample. Since the volumetric rings are 5 cm high, the penetrometer generates 300 readings per sample. For the calculation of SPRlab, an average of 180 readings is performed, excluding the first and last 60 readings of each sample. Samplings were carried out in the years 2016 and 2017. In 2016, 72 points were sampled, 24 points for each layer (0.00–0.10 m, 0.10–0.20 m and 0.20–0.30 m). In 2017, 270 points were sampled, 90 points for each layer. SPRfield was measured at each point and, simultaneously, beside the point where SPRfield was obtained, soil samples were collected to determine soil moisture and SPRlab. Soil penetration resistance measured in the laboratory (SPRlab), as a function of soil penetration resistance measured in the field (SPRfield) and soil moisture (U), was estimated using models generated by multiple linear regression (MLR), multiple nonlinear regression (MNLR) and radial-basis-function (RBF) and multilayer-perceptron (MLP) artificial neural networks (ANNs). Samples collected in 2017 (270) were used to calibrate the models, whereas those collected in 2016 (72) were used to validate them. Samples were collected at two years to evaluate the generalizability of the models, since the collection of samples in just one year can generate small data variability and generate models that are not generalist. In addition, due to the need for more data for the calibration phase, samples collected in 2017 were used to calibrate models and samples collected in 2016 to validate them. Models were calibrated with all sampled layers and stratified per layer. For the latter case (stratified per layer), samples were separated into two parts, one part with the surface layer (0.00–0.10 m) and the other with the subsurface layers (0.10–0.20 m and 0.20–0.30 m). Such procedure was carried out to check if there are better layers for soil compaction monitoring or if it does not depend on soil layer. Several crops such as soybean, corn, common bean, rice, peanuts and wheat have a high root depth up to 30 cm. Thus, the SPR can be monitored to a depth of 30 cm to monitor soil compaction and indicate possible agricultural managements. For this, in our study we stratified the 0.00–0.30 m layer into two layers: 0.00–0.10 m and 0.10–0.30 m. This was done because is difficult to study the properties of surface layer (0,00–0,10 m), due it is greatly affected by the soil texture and environment factors, which can lead to misinterpretations of the correct SPR values. Multiple linear and nonlinear regressions were calibrated and parameterized by the nonlinear GRG method (Abadie and Carpentier, 1969). ANNs were calibrated (trained) in the Intelligent Problem Solver mode of the program Statistica v.7. This mode allows several ANNs to be randomly trained, returning the quantity established previously based on those which showed lowest error. MLP ANNs were established with two hidden layers and number of neurons ranging from 8 to 40 in each layer, and the program returned 25 ANNs. The ANN with lowest root-mean-square error (RMSE) was selected for analysis. The training algorithm used was backpropagation, which is very robust for simulation of linear and nonlinear models (Haykin, 1994). The criterion to stop the calibration algorithm was the total number of cycles equal to 500 or mean square error lower than 1%. The activation function used was hyperbolic tangent (Eq. (1)).
2. Material and methods The data for the estimation of soil penetration resistance (SPR) determined in the laboratory (SPRlab) were obtained in an experimental area of the School of Agricultural and Veterinarian Sciences, São Paulo State University (Unesp), Brazil (21° 14′ 56″ S, 48° 16′ 52″ W, altitude of 572 m). According to Köppen’s classification, the climate of the region is Aw, subtropical, relatively dry in the winter, with summer rains, mean annual temperature of 22 °C and normal annual rainfall of 1425 mm (Alvares et al., 2013). The soil of the experimental area is classified as Eutrophic Red Oxisol (Soil Survey Staff, 2014). The soil of the experimental area had a particle-size distribution of 200 g kg−1 of sand, 290 g kg−1 of silt and 510 g kg−1 of clay (Claessen, 1997), being classified as clay (Soil Survey Staff, 2014). The geology of the area is located under the basalt of the Serra Geral Formation (IPT, 1981). The chemical analysis of the soil in the 0.00–0.20 m layer was: pH (CaCl2): 5.9, organic matter: 26 g dm−3, P: 43 mg dm−3, K: 4.7 mmolc dm−3, Ca: 44 mmolc dm−3, Mg: 23 mmolc dm−3, H + Al: 23 mmolc dm−3, sum of bases: 71.7 mmolc dm−3 e base saturation: 76%. The SPR measured in the field (SPRfield) was obtained by means of an automatic electronic penetrometer (PNT2000/M) attached to a fourwheeler (Suzuki Motors, LT-F160 QUAD-RUNNER model) and constructed according to the norm ASAE S313.3 (ASAE, 1999), in three soil layers (0.00–0.10 m, 0.10–0.20 m and 0.20–0.30 m). Soil samples for the determination of soil moisture (U) were collected beside the points where SPRfield was measured, and U was determined by the gravimetric method (Topp and Ferré, 2002). In this method, soil samples are first weighed and then taken in a forced circulation air oven at 105 °C to constant mass. After drying, they are weighed again and the moisture of each sample is calculated by the difference between the initial weight and the final weight divided by the final weight, the result being expressed in g water g soil−1. Close to the site where SPRfield and U values were obtained, an undisturbed sample was collected using volumetric rings (0.05 × 0.05 m), to determine SPRlab (Tormena et al., 1998). The volumetric rings for SPRlab determination were saturated by means of a
f(v) =
1 - e - av 1+e−av
where
f(v) = hyperbolic tangent activation function; 2
(1)
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a = estimate of the parameter which determines the hyperbolic tangent steepness; and, v = activation potential of the function.
Table 2 Number of neurons in each hidden layer of the models generated by artificial neural networks (ANNs) for each situation.
The RBF ANN has only one hidden layer, unlike the MLP, in which it is possible to choose the quantity of hidden layers. For RBF the number of neurons established for the hidden layer varied from 15 to 90 for the models with all layers and from 10 to 50 for the models stratified by layer. In each case, the ANN with lowest root-mean-square error (RMSE) was selected for analysis. The activation function for the RBF network is the radial basis function, defined by unsupervised techniques (Haykin, 1994). The statistical indices used to evaluate the accuracy of the SPRlab estimation models were the coefficient of determination (R2), rootmean-square error (RMSE) (Eq. (2)), mean bias error (MBE) (Eq. (3)) and Willmott’s index of agreement (d) (Willmott, 1981) (Eq. (4)). Outliers were removed according to the methodology proposed by Belsley et al. (1980).
i=1
(2)
N
∑ (Yobs i − Yesti) MBE =
i=1
(3)
N N
∑ (Yobs i − Yesti)2 d= 1−
i=1 N
∑ (|Yesti − Y¯| + |Yobs i − Y¯|)2 i=1
Number of neurons in each hidden layer
RBF
0.00–0.30 0.00–0.10 0.10–0.30
40 50 54
MLP
0.00–0.30 0.00–0.10 0.10–0.30
40–28 40–25 40–29
models as a function of SPRfield and U (Table 3). Firstly, the models were applied to all data of the three layers evaluated in the field (0.00–0.10; 0.10–0.20 and 0.20–0.30 m). Then, the samples of the 0.00–0.10 m layer were removed from the data set and the models were calibrated again. This procedure was carried out with the expectation that samples from the 0.00–0.10 m layer had high variability, which could interfere with the accuracy of the models. This was confirmed for the data observed in the calibration and validation, since the data of the 0.00–0.10 m layer showed higher standard error of the mean compared to the other layers (Table 3). According to the data of the mean, the values estimated by the models were very close to the observed ones, for the phases of both calibration and validation, except the data of validation of RBF ANN in the first layer, where the difference for the mean was higher than 0.3 MPa. In relation to maximum and minimum values, in an overall analysis between models for layers and phases (calibration and validation), the ANNs (MLP and RBF) had closer estimates than what was observed in the laboratory. The regressions (MLR and MNLR), in general, underestimated the maximum values observed, except for the MLR in the 0.10–0.30 m layer for the validation phase, and overestimated the minimum values, except for MNLR in the 0.00–0.30 m layer for the calibration phase, indicating lower amplitude in the estimation of SPRlab compared to the ANNs. The four models, applied to the data set evaluated in the 0.00–0.30 m layer, showed similar statistical indices of performance in the prediction accuracy between the calibration and validation phases, i.e., they showed generalization capacity and can be applied to other data sets (Fig. 1). However, when the models are compared, it can be observed that ANNs (RBF and MLP) showed higher accuracy than MLR and MNLR. Both the coefficient of determination (R2) and the error (RMSE) were better for the prediction by ANNs. In the overall mean of the calibration and validation phases of the models, the precision of ANNs (R2) was 86% higher and the error (RMSE) was 22% lower than those of the two multiple regressions. The accuracy between the ANNs (RBF and MLP) was similar. By using only the samples from the 0.00–0.10 m layer and applying the models, it can be noted that MLR and MNLR showed low accuracy in the prediction (Fig. 2), with lower precision and higher error compared to the situation in which the samples of all layers were used. In
N
N
Layer (m)
RBF – radial basis function; MLP – multilayer perceptron; Values for the RBF and MLP ANN models indicate number of neurons in the hidden layers.
∑ (Yobs i − Yesti)2 RMSE =
ANN model
(4)
where
N = total number of data in each model; Yobs i = observed values of Y; and, Yesti = estimated values of Y. 3. Results Four models were applied to assess the prediction accuracy in the estimation of values of soil penetration resistance (SPR) determined in the laboratory (SPRlab), with standardized moisture of the sample, based on the values of SPR determined in the field (SPRfield), with variable moisture (U) according to the local conditions. Multiple linear (MLR) and nonlinear (MNLR) regression models were calibrated for the data in different layers and applied to assess the accuracy in the validation data (Table 1). Artificial neural networks (ANNs) were applied in the estimation but, since there is definition of equations, the complexity of RBF and MLP ANNs was presented, indicating the number of neurons in the hidden layers for each situation (Table 2). Descriptive statistics was used in the data of soil penetration resistance determined in the laboratory (SPRlab) and estimated by the
Table 1 Equations calibrated for multiple linear and nonlinear regression models as a function of layers and applied to the validation data. Model
Layer (m)
Regression
MLR
0.00–0.30 0.00–0.10 0.10–0.30
SPRlab = 0.059 * SPRfield − 11.549 * U + 5.701 SPRlab = 0.518 * SPRfield − 5.807 * U + 3.971 SPRlab = 0.006 * SPRfield − 18.830 * U + 7.783
MNLR
0.00–0.30 0.00–0.10 0.10–0.30
SPRlab = 0.0008 * SPRfield2 − 166.369 * U2 + 0.042 * SPRfield + 77.985 * U − 6.274 SPRlab = -0.0012 * SPRfield2 − 147.908 * U2 + 0.237 * SPRfield + 73.711 * U − 6.584 SPRlab = 0.0124 * SPRfield2 − 77.643 * U2 − 0.039 * SPRfield + 23.053 * U + 2.175
MLR – multiple linear regression; MNLR – multiple nonlinear regression; SPRlab – soil penetration resistance measured in the laboratory (MPa); SPRfield – soil penetration resistance measured in the field (MPa); U – field soil moisture (g g−1). 3
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Table 3 Descriptive statistics for soil penetration resistance (SPR), measured in the laboratory (Observed), and estimated by the models for calibration and validation phases as a function of the layers used. Model
Calibration data 0.00–0.30 m
Validation data 0.00–0.10 m
0.10–0.30 m
0.00–0.30 m
0.00–0.10 m
0.10–0.30 m
2.74 2.77 2.76 2.75 2.72
Observed MLR MNLR RBF ANN MLP ANN
————————Mean – MPa———————— ————————Mean – MPa———————— 2.67 ± 0.03 2.46 ± 0.05 2.81 ± 0.03 2.79 ± 0.06 2.67 ± 0.02 2.46 ± 0.02 2.81 ± 0.02 2.68 ± 0.03 2.67 ± 0.02 2.46 ± 0.03 2.81 ± 0.02 2.66 ± 0.03 2.67 ± 0.02 2.47 ± 0.05 2.81 ± 0.03 2.70 ± 0.03 2.67 ± 0.02 2.47 ± 0.05 2.81 ± 0.03 2.72 ± 0.05
2.47 2.46 2.44 2.11 2.39
Observed MLR MNLR RBF ANN MLP ANN
————————Maximum – MPa—————— ————————Maximum – MPa———————— 4.46 3.29 4.46 3.99 3.24 2.78 3.33 3.56 3.07 2.71 3.27 3.02 3.73 3.29 4.24 3.26 3.85 3.23 4.16 4.28
3.24 2.71 2.69 3.18 3.13
3.99 4.20 3.72 3.59 4.21
Observed MLR MNLR RBF ANN MLP ANN
————————Minimum – MPa——————— ————————— Minimum – MPa———————— 1.37 1.37 1.86 1.80 1.90 2.14 2.04 2.12 1.36 1.68 1.95 1.91 1.65 1.54 1.85 2.17 1.82 1.59 1.93 2.09
1.81 2.23 2.12 0.93 1.15
2.01 2.17 2.11 2.13 1.87
± ± ± ± ±
0.08 0.03 0.04 0.12 0.09
± ± ± ± ±
0.06 0.05 0.05 0.06 0.07
MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. Mean values are followed by the standard error of the mean.
layers, and for soil tillage, providing environment for the development of the root system of crops. In addition, mapping of SPR may indicate areas of specific management (Oliveira Filho et al., 2015), reducing the time spent with the agricultural operation and consequently fuel consumption and use of labor, besides reducing CO2 emission from the agricultural operation. However, the definition of soil compaction by readings of soil penetration resistance taken in the field often leads to error, because these readings are influenced by soil moisture (Moraes et al., 2013). Because of that, studies have been conducted to generate models to estimate SPR with standardized moisture (Vaz et al., 2011; Silva et al., 2016). The spatial variability of SPR is influenced by soil moisture, and the higher the moisture content the lower the spatial dependence (Souza et al., 2006). Besides the moisture content, SPR is also influenced by soil texture, organic matter content and mineralogy (Vaz et al., 2013). Therefore, the models for SPR estimation with standardized moisture should be generated for each type of soil and, preferably, calibrated locally. Vaz et al. (2011), evaluating the accuracy of models in the prediction of SPRlab as a function of moisture, observed that model calibration for each type of soil and selection of the ideal model are fundamental for the estimation accuracy, since the precision may double with the correct choice. This can be observed in the present study, in which choosing the ANN model leads to higher accuracy of estimation compared to the others. Silva et al. (2016) proposed to estimate SPRlab based on soil moisture and density using nonlinear modeling. The precision observed by these authors (R2 = 0.68) was close to that obtained in the present study; however, operationally, the applied methodology is more expensive and time-consuming than that proposed here. In the methodology proposed by Silva et al. (2016), along the entire monitoring it is necessary to define soil density in the laboratory, which requires the collection of undisturbed soil samples. In the present study, after the calibration and validation of the models, SPRlab monitored is carried out by measurements taken in the field (SPRfield and moisture, simultaneously), using devices and sensors, such as the automatic electronic penetrometer (PNT2000/M) attached to a four-wheeler, which is very practical. Although there are studies to model SPRlab based on soil moisture (Vaz et al., 2011; Silva et al., 2016), none of them conducted an analysis of the layers which showed the best estimate. This becomes necessary
the calibration, the generated models were significant but there was no significance when the models were applied to another data set, since the statistical coefficients of the validation phase were very different from those of the calibration, indicating that models generated by MLR and MNLR cannot be applied to estimate SPRlab using data of the surface layer (0.00–0.10 m). For the ANNs, the calibration phase showed high accuracy, much higher than that observed using all samples. However, when the generated models were applied to the data of validation, the accuracy was greatly reduced, with statistical coefficients lower than those observed in the model with all samples. This indicates that all models generated for the surface layer (0.00–0.10 m) do not have generalization capacity, which can be explained by the greater variation of SPR in this layer, compared to the other data sets, as evidenced by the standard error of the mean for this layer (Table 3). For the models generated with data of the subsurface layers (0.10–0.30 m), it was observed that in the calibration phase the ANNs showed higher precision and lower error than the regressions (Fig. 3). Also for this phase, all models showed higher accuracy than that obtained with the data using all layers (Fig. 1) and the ANNs showed higher accuracy than MLR and MNLR. It can be noted that the R2 values of MLR and MNLR increased from the calibration phase to the validation phase, a fact not observed in the ANN models, in which the statistical indices of performance were similar between the phases. It is desirable that the values of the indices be similar when the model is applied to other data sets, since large differences may indicate low generalization by the model, especially when the values reduce the accuracy (Sargent, 2013). The difference in values between the calibration and validation phases did not reduce the accuracy of the models. However, the increased accuracy of the MLR and MNLR models may indicate low generalizability by these models. Based on the statistical indices of performance of the models, it is possible to observe that the estimation accuracy increased when the samples from the 0.00–0.10 m layer were removed for calibration and subsequent validation. 4. Discussion Mapping the soil penetration resistance (SPR) of agricultural areas is fundamental for the recommendation of subsoiling to break compacted 4
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Calibration
Validation
MLR
MNLR
RBF ANN
MLP ANN
Fig. 1. Performance graphs of the estimation of soil penetration resistance (SPR) for the models in the calibration and validation phases using all layers (0.00–0.30 m). MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. R2 – coefficient of determination; d – Willmott’s index of agreement; RMSE – root-mean-square error; MBE – mean bias error; ns – not significant; * significant at 0.05 probability level; ** significant at 0.01 probability level.
readings is expected in this layer, as SPRfield is influenced by soil moisture and the loss of water in agricultural areas is not uniform (Colombi et al., 2018). Additionally, the variation may occur according to the plant material and amount of straw present on soil surface, interfering with SPRfield readings in surface layers (Valadão Júnior et al., 2014). Although the soil surface layer (0.00–0.10 m) concentrates a large
because a certain layer may not be technically adequate for the prediction, a fact observed in the present study, in which the accuracy increased when the samples from the surface layer (0.00–0.10 m) were removed for calibration of the models. Therefore, samples from the 0.10–0.30 m layer are recommended for SPRlab monitoring. Since most of the root system of crops and spontaneous vegetation in agricultural areas is concentrated in the surface layer, a large variation in SPRfield 5
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Calibration
Validation
MLR
MNLR
RBF ANN
MLP ANN
Fig. 2. Performance graphs of the estimation of soil penetration resistance (SPR) for the models in the calibration and validation phases using the 0.00–0.10 m layer. MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. R2 – coefficient of determination; d – Willmott’s index of agreement; RMSE – root-mean-square error; MBE – mean bias error; ns – not significant; * significant at 0.05 probability level; ** significant at 0.01 probability level.
to misunderstandings (Bonnin et al., 2010; Pias et al., 2018). Thus, as the roots of the crops develop to deeper layers (30–40 cm), the monitoring of SPR in subsurface layers (0.10–0.30 m) is an alternative in monitoring soil compaction and indicating of possible agricultural managements (Alesso et al., 2019). In the present study, the definition of models was carried out under specific conditions, such as the soil type used, equipment used for
amount of roots, most crops such as corn, soybean, common bean, rice, sugarcane and wheat have effective root depths of 30 to 40 cm deep in the soil (Allen et al., 1998). Effective root depth represents the soil layer where 80% of the total plant roots are concentrated. Due to factors such as soil moisture, temperature, radiation and machine traffic, the surface layer presents high variability, which makes it difficult to monitor soil compaction through SPR readings on the surface layer, which may lead 6
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Calibration
Validation
MLR
MNLR
RBF ANN
MLP ANN
Fig. 3. Performance graphs of the estimation of soil penetration resistance (SPR) for the models in the calibration and validation phases using the 0.10–0.30 m layer. MLR – multiple linear regression; MNLR – multiple nonlinear regression; RBF ANN – radial-basis-function artificial neural network; MLP ANN – multilayer-perceptron artificial neural network. R2 – coefficient of determination; d – Willmott’s index of agreement; RMSE – root-mean-square error; MBE – mean bias error; ns – not significant; * significant at 0.05 probability level; ** significant at 0.01 probability level.
and the type of soil used, the models can be recommended and present application in any locations. This can be done both to indicate the best soil layers for the highest accuracy, as well as to recommend the models for applications elsewhere. Thus, we recommend using the methodology proposed in the present study for each area and then applying the generated models to monitor the spatial variation of SPRlab, in possible zones of specific management, with the devices used in the calibration of the models. However, as SPR is influenced by soil texture (Moraes et al., 2013), in
SPRlab and SPRfield readings, model types and soil layers used. If there is a change in any characteristic of the methodology, such as sampled soil layers, devices used to evaluate soil moisture and SPRfield, device to measure SPRlab etc., the accuracy of the results should be checked, possibly requiring calibration of new models. The studies of Hernanz et al. (2000); Valadão Júnior et al. (2014) demonstrate that, in which the size of the base of the cone used to measure SPRfield significantly influences the values; smaller bases increase SPRfield values. However, under conditions similar to the present study regarding the equipment 7
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Declaration of Competing Interest
areas where clay content is similar to that of the soil evaluated in the present study, one can use the models calibrated here for SPRlab prediction using SPRfield and U measures. In relation to the models, it can be observed that ANNs showed higher accuracy than MLR and MNLR, and no relevant differences were observed between the types of ANN (RBF or MLP). For having the capacity to recognize patterns within data sets, studies have demonstrated that ANNs have higher prediction accuracy than other models and may show a 40% higher precision (Yilmaz and Kaynar, 2011; Kashi et al., 2014). According to statistical indices and depending on generalizability, some models are more suitable for certain data sets than others. So, we found in the present study that the ANNs models presented higher precision (R2) and lower error (RMSE) than MLR and MNLR models. Thus, ANNs are more accurate models and should be indicated for the estimation of SPR. In addition, another key step in choosing the best models is the similarity of accuracy between the calibration and validation phases. Models that present very different statistical indices values between the calibration and validation phases tend to be less generalist and more likely to error (Sargent, 2013). Usually, MLP ANNs have high estimation accuracy, being superior to RBF ANNs (Paschalidou et al., 2011; Kashi et al., 2014). Due to their architecture with more than one hidden layer, these models are more generalist and their application in other data sets is more recommended compared to RBF ANNs (Haykin, 1994). Nonetheless, this fact was not observed in the present study, and both models are recommended for SPRlab estimation. Depending on the data set and objective of the study, RBF or MLP ANNs can be indicated. When the data have large variability of error, RBF ANNs are more recommended than MLP ANNs because they have activation functions that reduce the amplitude of errors (Xie et al., 2011). However, according to the authors, if the problem is more linearly separable, MLP ANNs are recommended because of their more complex structure, capable of better recognizing data patterns. For the present study, MLP and RBF ANNs had similar accuracies and were recommended for SPRlab estimation. In addition, samples from the 0.10–0.30 m layer are recommended for the calibration of the models and subsequent application to estimate SPRlab. SPRfield determination with variable moisture limits the comparison of SPR values. In the same area of the present study, Chioderoli (2013) evaluated SPRfield and soil moisture (U) before the sowing of corn (SPRfield = 2.70 MPa and U = 0.27 g g−1) and after its harvest (SPRfield = 2.08 MPa and U = 0.37 g g−1). This author observed that SPRfield values were higher before sowing than after harvest, which may indicate a possible beneficial effect of corn for soil decompaction. However, when the model generated by MLP ANN for soil samples collected in the 0.10–0.30 m layer, proposed in the present study, was applied using the SPRfield and U values presented by Chioderoli (2013), it could be observed that, with standardized soil moisture, SPRlab was similar for both periods, 2.73 MPa before corn sowing and 2.77 MPa after its harvest. Therefore, it is fundamental to obtain SPR with standardized moisture in order to allow for the comparison between SPR values determined along the production cycle of several crops, in order to assess the influence of the various management systems on soil physical quality.
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments The authors thank the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) for granting the scholarships to the first, third and fifth authors, and the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) for granting the scholarship to the second author. References Abadie, J., Carpentier, J., 1969. Generalization of the wolf reduced gradient method to the case of nonlinear constraints. In: Optimization. R. Fletcher 9ed, Academic Press, New York, pp. 37–47. Alesso, C.A., Masola, M.J., Carrizo, M.E., Cipriotti, P.A., Imhoff, S.D., 2019. Spatial variability of short-term effect of tillage on soil penetration resistance. Arch. Agron. Soil Sci. 65, 822–832. https://doi.org/10.1080/03650340.2018.1532076. Allen, R.G., Pereira, L.S., Raes, D., Smith, M., 1998. Crop evapotranspiration-Guidelines for computing crop water requirements-FAO Irrigation and drainage paper 56. Fao, Rome 300 (9), D05109. Alvares, C.A., Stape, J.L., Sentelhas, P.C., de Moraes, G., Leonardo, J., Sparovek, G., 2013. Köppen's climate classification map for Brazil. Meteorol. Z. 22, 711–728. https://doi. org/10.1127/0941-2948/2013/0507. American society of agricultural engineers (ASAE), 1999. Agricultural Machinery Management. EP 496.2. In: ASAE standards: Standards engineering practices data. American Society of Agricultural Engineers, St. Joseph, pp. 353–358. Belsley, D.A., Kuh, E., Welsch, R.E., 1980. Regression diagnostics: Identifying influential data and sources of collinearity, 1st ed. John Wiley & Sons, New York, pp. 100p. Bonnin, J.J., Mirás-Avalos, J.M., Lanças, K.P., González, A.P., Vieira, S.R., 2010. Spatial variability of soil penetration resistance influenced by season of sampling. Bragantia 69, 163–173. https://doi.org/10.1590/S0006-87052010000500017. Chioderoli, C.A., 2013. Intercropping of Urochloas with maize in no-tillage system cultivated before summer soybean. Universidade Estadual Paulista – Faculdade de Ciências Agrárias e Veterinárias de Jaboticabal, pp. 200 Doctoral thesis. Claessen org., M.E.C., 1997. Manual de métodos de análise de solo, 2nd ed. Centro Nacional de Pesquisa de Solos, Rio de Janeiro. Colombi, T., Torres, L.C., Walter, A., Keller, T., 2018. Feedbacks between soil penetration resistance, root architecture and water uptake limit water accessibility and crop growth–A vicious circle. Sci. Total Environ. 626, 1026–1035. https://doi.org/10. 1016/j.scitotenv.2018.01.129. Haykin, S., 1994. Neural networks: a comprehensive foundation, 2nd ed. Prentice-Hall, Englewood Cliffs, NJ. Hernanz, J.L., Peixoto, H., Cerisola, C., Sánchez-Girón, V., 2000. An empirical model to predict soil bulk density profiles in field conditions using penetration resistance, moisture contente and soil depth. J. Terramechanics. 37, 167–184. https://doi.org/ 10.1016/S0022-4898(99)00020-8. IPT – Instituto de Pesquisas Tecnológicas do Estado de São Paulo. 1981. Mapa geomorfológico do Estado de São Paulo 1981. São Paulo, pp. 94. Kashi, H., Emamgholizadeh, S., Ghorbani, H., 2014. Estimation of soil infiltration and cation exchange capacity based on multiple regression, ANN (RBF, MLP), and ANFIS models. Commun. Soil Sc. Plant An. 45, 1195–1213. https://doi.org/10.1080/ 00103624.2013.874029. Moraes, M.T.D., Debiasi, H., Franchini, J.C., Silva, V.R.D., 2013. Soil penetration resistance in a rhodic eutrudox affected by machinery traffic and soil water content. Eng. Agric. 33, 748–757. https://doi.org/10.1590/S0100-69162013000400014. Oliveira, P.D.D., Sato, M.K., Lima, H.V.D., Rodrigues, S., Silva, A.P.D., 2016. Critical limits of the degree of compactness and soil penetration resistance for the soybean crop in N Brazil. J. Plant Nutr. Soil Sc. 179, 78–87. https://doi.org/10.1002/jpln. 201400315. Oliveira Filho, F.X., Miranda, N.D.O., Medeiros, J.F., Silva, P., Mesquita, F.O., Costa, T.K., 2015. Management zones for subsoiling of a sugarcane field. Rev. Bras. Eng. Agric. Amb. 19, 186–193. https://doi.org/10.1590/1807-1929/agriambi.v19n2p186-193. Paschalidou, A.K., Karakitsios, S., Kleanthous, S., Kassomenos, P.A., 2011. Forecasting hourly PM 10 concentration in Cyprus through artificial neural networks and multiple regression models: implications to local environmental management. Environ. Sci. Pollut. R. 18, 316–327. https://doi.org/10.1007/s11356-010-0375-2. Pias, O.H.D.C., Cherubin, M.R., Basso, C.J., Santi, A.L., Molin, J.P., Bayer, C., 2018. Soil penetration resistance mapping quality: effect of the number of subsamples. Acta Scient. Agro. 40, e34989. https://doi.org/10.4025/actasciagron.v40i1.34989. Sargent, R.G., 2013. Verification and validation of simulation models. J. Simul. 7, 12–24. Silva, W.M.D., Bianchini, A., Cunha, C.A.D., 2016. Modeling and correction of soil penetration resistance for variations in soil moisture and soil bulk density. Eng. Agric. 36, 449–459. https://doi.org/10.1590/1809-4430-Eng.Agric.v36n3p449-459/2016. Soil Survey Staff, 2014. Soil taxonomy, 12th ed. USDANRCS, Washington DC, USA, Washington DC. Souza, Z.M.D., Campos, M.C.C., Cavalcante, Í.H.L., Marques Júnior, J., Cesarin, L.G.,
5. Conclusions Soil penetration resistance measured in the laboratory can be estimated with high accuracy based on soil penetration resistance and soil moisture measured in the field. Models with data from the surface layer (0.00–0.10 m) are not recommended to estimate soil penetration resistance measured in the laboratory. Artificial neural networks have higher estimation accuracy than multiple linear and nonlinear regressions. We recommend the use of models generated by artificial neural networks (MLP or RBF) and samples from the 0.10–0.30 m layer for the monitoring of soil penetration resistance. 8
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penetration resistance for varying soil water content. Geoderma 166, 92–101. https://doi.org/10.1016/j.geoderma.2011.07.016. Vaz, C.M., Manieri, J.M., Maria, I.C., 2013. Scaling the dependency of soil penetration resistance on water content and bulk density of different soils. Soil Sci. Soc. Am. J. 77, 1488–1495. https://doi.org/10.2136/sssaj2013.01.0016. Willmott, C.J., 1981. On the validation of models. Phys. Geogr. 2, 184–194. Xie, T., Yu, H., Wilamowski, B., 2011. Comparison between traditional neural networks and radial basis function networks. In: IEEE International Symposium on Industrial Electronics (ISIE). IEEE, pp. 1194–1199. Yilmaz, I., Kaynar, O., 2011. Multiple regression, ANN (RBF, MLP) and ANFIS models for prediction of swell potential of clayey soils. Expert Syst. Appl. 38, 5958–5966. https://doi.org/10.1016/j.eswa.2010.11.027.
Souza, S.R.D., 2006. Spatial variability of soil penetration resistance and soil moisture at different periods of sampling under sugarcane crop. Cienc. Rural. 36, 128–134. https://doi.org/10.1590/S0103-84782006000100019. Topp, G.C., Ferré, P.A., 2002. The soil solution phase. In: Dane, J.H., Topp, G.C. (Eds.), Methods of Soil Analysis, Part 4, Physical Methods. Soil Science Society of America Inc, Madison, pp. 417–1074. Tormena, C.A., Silva, A.P., Libardi, P.L., 1998. Characterization of the least limiting water range of an oxisol under no-tillage. Rev. Bras. Cienc. Solo. 22, 573–581. https://doi. org/10.1590/S0100-06831998000400002. Valadão Junior, D.D., Biachini, A., Valadão, F.C.A., Rosa, R.P., 2014. Penetration resistance according to penetration rate, cone base size and different soil conditions. Bragantia 73, 171–177. https://doi.org/10.1590/brag.2014.013. Vaz, C.M., Manieri, J.M., Maria, I.C., Tuller, M., 2011. Modeling and correction of soil
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