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Engenharia Agrícola

versão impressa ISSN 0100-6916versão On-line ISSN 1809-4430

Eng. Agríc. vol.39 no.4 Jaboticabal jul/agosto 2019  Epub 12-Ago-2019

http://dx.doi.org/10.1590/1809-4430-eng.agric.v39n4p444-456/2019 

Scientific Papers

Soil and Water Engineering

PEDOFUNCTIONS APPLIED TO THE LEAST LIMITING WATER RANGE TO ESTIMATE SOIL WATER CONTENT AT SPECIFIC POTENTIALS

Renan F. R. Tavanti1* 
http://orcid.org/0000-0002-4496-9660

Onã da S. Freddi2 

Tauan R. Tavanti3 

Adriel Rigotti2 

Wellington de A. Magalhães4 

2 Universidade Federal de Mato Grosso - UFMT/ Sinop - MT, Brasil.

3 Universidade Estadual Paulista "Júlio de Mesquita Filho" - UNESP/ Ilha Solteira - SP, Brasil.

4 Universidade Federal de Mato Grosso - UFMT/ Cuiabá - MT, Brasil.


ABSTRACT

The least limiting water range (LLWR) is a soil physical quality indicator that receives much attention. It has been criticized and put to the test regarding mathematical models that compose it since they describe the behavior of soil physical attributes in a simplified way. This study aimed to assess the efficiency of some pedofunctions proposed in the literature and artificial neural networks on the accuracy in predicting soil water retention at potentials equivalent to field capacity (θFC) and permanent wilting point (θPWP). In other words, to apply the best models to LLWR of two soil types (Oxisol and Ultisol) and verify changes in their structure. The results indicated that pedofunctions using sand, silt, clay, bulk density, and soil organic matter contents are more efficient in estimating θFC and θPWP. However, the use of multiple linear regression models to predict θFC values below 0.20 m3 m−3 may present a slight tendency to overestimate it, which is not observed in the neural networks. As in R2, equations from neural networks were more efficient in estimating θFC and θPWP. Pedofunctions used to calculate LLWR differ in the establishment of the critical soil bulk density, exposing the limitations of the model.

Key words: Soil physics; soil physical quality indicator; available water; pedotransfer functions; artificial neural networks

INTRODUCTION

Soil physical quality cannot be measured directly, but it is assessed through attributes such as porosity, bulk density, penetration resistance, and water content available to plants (Guimarães et al., 2013). Soil physical quality was better investigated by Letey (1985), who proposed the concept of 'non-limiting water range', which integrates the relationships between soil attributes and water content available to plants. Silva et al. (1994) improved this concept when assembling mathematical models for estimating soil moisture in the field capacity, permanent wilting point, air-filled porosity, and soil penetration resistance, originating a soil structural quality indicator known as least limiting water range. Tormena et al. (1998) later introduced this indicator in Brazil as Intervalo Hídrico Ótimo.

The least limiting water range (LLWR) has been received much attention in Brazil and applied in several studies. Among them, Freddi et al. (2009) assessed compaction levels of an Oxisol and its physical quality reduction processes, as well as yield reduction of two maize hybrids as a response to compaction. The authors verified that, at certain levels of soil bulk density, water content should be above the field capacity to avoid limitations due to soil penetration resistance and meet the water requirements of hybrids. In this case, the intense machinery traffic led to soil structural degradation. In addition, the authors proposed soil decompaction actions when bulk density reached 1.46 Mg m−3, considered as critical in LLWR. Betioli Junior et al. (2012) analyzed an Oxisol after 30 years of no-tillage and observed a decrease in LLWR due to an increase in bulk density, regardless of the used critical soil penetration resistance, which was 2 MPa.

Despite the studies that consolidate LLWR as a soil physical quality indicator, it has been criticized and its validity put to the test by several authors (Gubiani et al., 2013, Jong Van Lier & Gubiani, 2015; Cecagno et al., 2016). These studies have questioned the efficiency of the linear mathematical model used to determine LLWR since the relationships between soil attributes are not linear and describe them in a relatively simple way is still one of the challenges of soil physics (Klein et al., 2016; Jong Van Lier & Gubiani, 2015).

Over the years, researchers have been proposing mathematical models to estimate soil water retention using attributes that correlate directly with one another, such as clay, silt, sand, soil organic matter content, and bulk density (Barros et al., 2013; Medrado & Lima, 2014; Medeiros et al., 2014). These models are also known as pedofunctions or pedotransfer functions (PTF) and can be applied to LLWR.

Most models currently available were developed for temperate regions (Gupta & Larson, 1979; Rawls et al., 1982; Saxton et al., 1986), where edaphoclimatic properties and soil mineralogical characteristics are different from tropical regions. For Brazil, some models have already been established (Reichert et al., 2009, , Barros et al., 2013, , Medeiros et al., 2014), but their validity in soils submitted to agricultural management different from those of the original database may make them unsuitable for use.

In the case of complex systems, mathematical modeling techniques may be more efficient in predicting soil water content, such as artificial neural networks (ANN) (Jana et al., 2012; Jana & Mohanty, 2012; Nguyen et al., 2017). ANNs have shown high performance due to factors such as robust and parallel distributed structure (layers of neurons), generalization and learning efficiency that make them capable of solving complex problems (Leal et al., 2015). In addition, they are tolerant to outliers, in which they are normalized in the layers of neurons, allowing the modeling of distinct variables and their non-linear relationships. This computational technique simulates the neural structure of intelligent organisms, which acquire knowledge through the experience and acquisition of punctual information.

As an example of the application of ANNs in agricultural research, Leal et al. (2015) reported their efficiency to estimate maize grain yield through soil attributes such as particle size distribution, soil organic matter content, cation exchange capacity, and base saturation. Ebrahimi et al. (2019) compared the efficiency of mathematical models in the estimates of the biological parameters of soil microbiota from their attributes and verified that ANN was more efficient than multiple linear regressions.

Based on these observations, this study aimed to assess the efficiency of some PTFs proposed in the literature and ANNs on the accuracy in predicting soil water retention at potentials equivalent to field capacity (θFC) and permanent wilting point (θPWP). In other words, to apply the best models to LLWR of two soil types (Oxisol and Ultisol) and verify changes in their structure.

MATERIAL AND METHODS

The data were obtained from two representative soils of the Mato Grosso State, Brazil, classified according to the Brazilian Soil Classification System (Embrapa, 2013) as a Dystrophic Red-Yellow Latosol and Dystrophic Red-Yellow Argisol, located at the geographical coordinates 59°11′59.0″ W and 12°35′49″ S and 56°01′16.8″ W and 9°54′04″ S, with an altitude of 350 and 283 m, respectively. According to the U.S. Department of Agriculture (Soil Survey Staff, 2014), the soils are classified as Oxisol and Ultisol, respectively. We will use in this study the USDA classification for standardization purposes.

These soils were sampled from October 2015 to August 2016. The Oxisol was under integrated crop-livestock systems, with an intense crop rotation consisting of soybean as main crop and maize as the second crop intercropped with forage species of the genus Urochloa. In some situations, millet or sorghum was chosen instead of maize as the second crop. The forage crops subsidized livestock farming during the dry season until the beginning of rains. The mean annual stocking rate was 2 animals of 450 kg ha−1 year−1.

The Ultisol was under Brachiaria brizantha cv. Marandu for more than ten years managed for extensive livestock farming, which was not subjected to any soil tillage. The mean annual stocking rate was 1.5 animals of 450 kg ha−1 year−1.

Soil physical and chemical attributes were determined from 156 undisturbed and 30 disturbed soil samples. Disturbed soil samples were collected at depths of 0–0.10 and 0.10–0.20 m with a Dutch auger. Undisturbed soil samples were taken using stainless steel volumetric rings with 5 cm high × 5 cm in diameter (98.17 cm3) from trenches at depths of 0–0.10 and 0.10–0.20 m.

Disturbed soil samples were taken to the laboratory, air dried, and sieved in 200 mm diameter stainless steel mesh sieves. Thus, particle size distribution was determined by the pipette method and organic matter contents (OM) by potassium dichromate oxidation (Embrapa, 2011). Undisturbed soil samples were saturated with water in plastic trays and subjected to tensions of 0, 30, 60, and 100 hPa in a sandbox and 300, 600, 1000, 5000, and 15000 hPa in pressure chambers with a porous plate. After each potential had reached moisture balance, the samples were weighed in order to find the water content. Subsequently, they were subjected to penetration resistance (PR), determined by a bench electronic penetrometer. The penetrometer had the following characteristics: load cell of 20 kg, penetration pin of 3 mm with 4 mm tip in a cone shape with 30° angle, and tip base area of 7.06 mm2. The constant penetration rate was 10 mm min−1, with two replications per sample, totaling 180 readings per replication. Therefore, the PR data taken from the first centimeter at the top and bottom of the rings were discarded. Thus, each microprofile consisted of PR readings recorded along a vertical transect of 3 cm, acquired from 1 to 4 cm deep, within a core of 5 cm of soil height, in accordance with the representative elementary volume theory. The PR value of each soil sample was obtained from the overall mean of records.

Subsequently, the undisturbed soil samples were oven-dried at 105 °C for 24 hours. The total porosity (TP), bulk density (BD), and soil water content at each tension were calculated (Embrapa, 2011).

For LLWR construction, the model proposed by Busscher (1990) was used to build the PR curve. The water content in which soil penetration resistance is limiting to root growth was obtained by [eq. (1)]:

PR = PRcexpβ1 × BDβ21β3 (1)

Where:

θPR is the volumetric soil water content in which PR reaches the critical value (m3 m−3);

BD is the soil bulk density (Mg m−3);

PRc is the critical PR value, and

β1, β2, and β3 are the adjustment parameters of the equation. The PRc value of 2 MPa proposed by Taylor et al. (1966) was used.

The water content in which aeration porosity is 10%, i.e., air-filled capacity (θAFC), was found through [eq. (2)]:

AFC = TP - 0.1 2 (2)

Where:

TP is the total porosity (m3 m-3).

For the other LLWR curves corresponding to θFC and θPWP, the pedofunctions proposed by several authors were used, as shown in Tables 1 and 2, respectively.

TABLE 1 Source of pedotransfer functions used to estimate soil water content in the field capacity (θFC). 

Source Soil Model1 R2
Oxisol
Silva et al. (1994) CAN θFC = exp -0.873* BD 0.511* 100 -0.115 0.96*
Gupta & Larson (1979) USA θFC = 0.001* SD + 0ns ST + 0ns CL + 0ns OM + 0.179* BD 0.99*
Rawls et al. (1982) USA θFC = – 0.588* + 0ns SD + 0ns ST + 0.027* CL + 0ns OM + 0ns BD 0.74*
Saxton et al. (1986) USA θFC = exp[( – 1.335* – ln A)/ B] 0.57*
Ritchie et al. (1999) USA GM = 0.169* (CL/SD) 0.405* → θFC = GM × BD 0.47*
Arruda et al. (1987) BRA θFC = 0.040* + 0ns (CL+ST) + 1.22×10-4* (CL+ST)2 0.74*
van den Berg et al. (1987) TRP θFC = -1.752* + 0.053* CL + 0ns ST + 0.132* OM 0.74*
Oliveira et al. (2002) BRA θFC = 0.015* ST + 0.003* CL 0.99*
Ultisol
Silva et al. (1994) CAN θFC = exp -0.951* BD -0.163* 100 -0.124* 0.34*
Gupta & Larson (1979) USA θFC = 0ns SD + 0ns ST + 0ns CL + 0.017* OM + 0.109* BD 0.99*
Rawls et al. (1982) USA θFC = 0.3820.003* SD + 0ns ST + 0ns CL + 0ns OM + 0ns BD 0.72*
Saxton et al. (1986) USA θFC = exp[(– 0.665* – ln A)/ B] 0.60*
Ritchie et al. (1999) USA GM = 0.255* (CL/SD) 0.167* → θFC = GM × BD 0.01*
Arruda et al. (1987) BRA θFC = 0.107* + 0.003* (CL+ST) + 0ns (CL+ST)2 0.72*
van den Berg et al. (1987) TRP θFC = 0ns + 0ns CL + 0ns ST + 0ns OM -
Oliveira et al. (2002) BRA θFC = 0.004* ST + 0.006* CL 0.97*

1 CAN: Canadian soils, BRA: Brazilian soils, USA: American soils, TRP: Tropical soils; CL: clay (dag kg-1), ST: silt (dag kg-1), SD: sand (dag kg-1), BD: bulk density (g cm-3), OM: organic matter (dag kg-1), GM: gravimetric moisture at -100 or -15000 hPa (kg kg-1); A = exp[ – 4.396 – 0.0715 CL – 4.88×10-4 (SD2) – 4.28×10-5 (SD2) CL]; B = – 3.14 – 0.002 (CL2) – 3.48×10-5 (SD2) CL.

TABLE 2 Source of pedotransfer functions used to estimate soil water content in the permanent wilting point (θPWP). 

Source Soil Model1 R2
Oxisol
Silva et al. (1994) CAN θPWP = exp -0.873* BD 0.511* 15000 -0.115 0.96*
Gupta & Larson (1979) USA θPWP = 0ns SD – 0.017* ST + 0.010* CL + 0ns OM + 0ns BD 0.99*
Rawls et al. (1982) USA θPWP = 1.034* + 0ns SD – 0.099* ST + 0ns CL + 0ns OM + 0ns BD 0.95*
Ritchie et al. (1999) USA θPWP = θpwp*1.35×10-10* exp (0.285* SD) 0.90*
Arruda et al. (1987) BRA θPWP = – 0.382* + 0.013* (CL+ST) 0.94*
van den Berg et al. (1987) TRP θPWP= 1.034* + 0ns CL – 0.099* ST 0.95*
Oliveira et al. (2002) BRA θPWP = 0ns SD – 0.017* ST + 0.010* CL + 0ns BD 0.99*
Ultisol
Silva et al. (1994) CAN θPWP = exp -0.951* BD -0.163* 15000 -0.124* 0.34*
Gupta & Larson (1979) USA θPWP = 0ns SD + 0ns ST + 0.003* CL + 0.019* OM + 0.020* BD 0.99*
Rawls et al. (1982) USA θPWP = 0.293*0.002* SD + 0ns ST + 0ns CL + 0ns OM + 0ns BD 0.70*
Ritchie et al. (1999) USA θPWP = θpwp*2.51×10-5* exp (0.087* SD) 0.78*
Arruda et al. (1987) BRA θPWP = 0.088* + 0.002* (CL+ST) 0.70*
van den Berg et al. (1987) TRP θPWP= 0.088* + 0.002* CL + 0.002* ST 0.70*
Oliveira et al. (2002) BRA θPWP = 0ns SD + 0.003* ST + 0.005* CL + 0ns BD 0.97*

1 CAN: Canadian soils, BRA: Brazilian soils, USA: American soils, TRP: Tropical soils; CL: clay (dag kg-1), ST: silt (dag kg-1), SD: sand (dag kg-1), BD: bulk density (g cm-3), OM: organic matter (dag kg-1), GM: gravimetric moisture at -100 or -15000 hPa (kg kg-1), θpwp*: mean water content at the permanent wilting point (m3 m-3).

The multilayer perceptron ANN was also tested. For this, 75% of the data were used for ANN training and 25% for validation. The supervised learning was used with two sets of values, i.e., input and output values. Training

consisted of a parameter optimization problem (synaptic weights) to respond to the inputs as expected until the error between observed and estimated values generated by ANNs reached the desired minimum value, i.e., close to zero (Leal et al., 2015).

The ANNs consisted of entries (inputs) corresponding to the soil attributes sand (SD), silt (SIL), clay (CL), BD, and OM. Outputs (response variables) were the respective soil water contents equivalent to θFC and θPWP. We chose the composition of two hidden layers, one with seven neurons and other with five neurons, respectively. Thus, the ANN architecture could be described as 5-7-5-2 (Figure 1). The activation function used was the hyperbolic tangent, as described in [eq. (3)]:

FIGURE 1 Artificial neural network architecture (5-7-5-2) used to estimate θFC and θPWP in an Oxisol (A) and Ultisol (B). Circles with letter B indicate the biases assigned to each layer of neurons, and I, H, and O indicate input attributes, neurons, and outputs of θFC and θPWP, respectively. 

TanH = sinh xcosh x 3 (3)

Where:

TanH is the hyperbolic tangent;

sinh is hyperbolic sine,

cosh is hyperbolic cosine.

The data were submitted to the Shapiro & Wilk normality test (p> 0.05) using the software R (R Development Core Team, 2015). Outliers with values 2.5 times higher than the interquartile range were removed, respecting the limit of 10% of the total observations of each treatment (soil type). Subsequently, a descriptive analysis was performed by calculating the mean, median, minimum, and maximum, standard deviation, coefficient of variation (CV), skewness, and kurtosis. The proposed pedofunctions were adjusted for the respective data sets. The neuralnet package was accessed for ANN training following the previously described criteria for assembly of its structure, using the “plotnet” function for network plotting.

The highest coefficient of determination (R2) and lowest mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) were used in order to compare the efficiency of pedofunctions in predicting values.

MSE = 1n Σi=1n ei-mi2 4 (4)

RMSE = 1n Ʃi=1nei - mi2 5 (5)

MAPE = Ʃi=1n ei -miƩi=1n mi × 100 6 (6)

Where:

n is the number of sampling points;

ei is the value estimated by the pedofunctions, and

mi is the measured value (observed).

RESULTS AND DISCUSSION

Both soils showed a high BD, with mean values of 1.356 and 1.505 Mg m−3 for the Oxisol and Ultisol, respectively (Table 3). Variations of minimum and maximum values of 0.920 and 1.545 Mg m−3 for the Oxisol and 1.180 and 1.760 Mg m−3 for the Ultisol indicated the existence of potentially compacted sites and sites with a structure not affected by management systems. Based on DB for the construction of pedofunctions, this variability is desirable, as they perform estimates with a wide range of values under previously non-sampled conditions. According to Gomes (2000), the variability of the assessed attributes can be classified according to the magnitude of their coefficient of variation (CV), being considered low when CV is lower than 10%, medium when CV is between 10 and 20%, high when CV is between 20 and 30%, and very high when CV is higher than 30%. Thus, BD variability of the Oxisol was classified as medium, and that of the Ultisol was considered low (14.97 and 8.63%, respectively).

TABLE 3 Descriptive analysis of soil physical and chemical attributes of an Oxisol and Ultisol at a depth of 0.00–0.10 m.1 

Attributes2 Mean Median Min Max SD CV Kurt Asym Pw<W
Oxisol
SD (dag kg-1) 55.341 58.335 52.419 62.424 3.236 5.847 0.057 1.246 0.001*
SIL (dag kg-1) 12.527 9.096 8.097 14.266 1.986 15.850 0.185 -1.287 0.001*
CL (dag kg-1) 32.131 32.744 29.479 33.315 1.250 3.890 -0.130 -1.181 0.002*
OM (dag kg-1) 2.554 2.411 2.333 3.087 0.244 9.553 0.045 1.242 0.001*
BD (Mg m-3) 1.356 1.458 0.920 1.545 0.203 14.970 -0.054 -1.209 0.001*
θFC (m3 m-3) 0.285 0.293 0.212 0.346 0.039 13.684 -0.545 -0.558 0.248ns
θPWP (m3 m-3) 0.160 0.168 0.132 0.172 0.014 8.750 -0.170 -1.275 0.000*
Ultisol
SD (dag kg-1) 65.736 64.900 50.500 81.000 7.019 10.638 0.666 0.502 0.242ns
SIL (dag kg-1) 10.932 8.500 1.700 18.900 4.400 36.363 -0.339 -0.268 0.880ns
CL (dag kg-1) 22.800 22.300 9.700 39.500 6.560 26.315 0.949 0.296 0.461ns
OM (dag kg-1) 3.649 3.562 1.860 7.240 1.546 42.356 -0.289 0.776 0.046*
BD (Mg m-3) 1.505 1.361 1.180 1.760 0.138 8.637 0.804 -0.802 0.170ns
θFC (m3 m-3) 0.210 0.209 0.160 0.260 0.043 20.476 -2.214 -0.265 0.002*
θPWP (m3 m-3) 0.160 0.160 0.130 0.220 0.032 20.00 0.563 0.926 0.021*

1 Min: minimum, Max: Maximum, SD: standard deviation, CV: coefficient of variation (%), Kurt: kurtosis, Asym: asymmetry, Pw<W: p-value of Shapiro-Wilk’s test. 2 CL: clay, ST: silt, SD: sand, BD: bulk density, OM: organic matter, Θfc: soil water content in the field capacity, Θpwp: soil water content in the permanent wilting point.

The texture of both soils was classified as medium, but the Oxisol presented a higher clay content (Table 1). The range of CL values varied from 29.479 to 33.315 dag kg−1 for the Oxisol and 9.700 to 39.500 dag kg−1 for the Ultisol, justifying the CV values classified as low and high, respectively. Despite the low variability of clay content in the Oxisol, these values are supposed to be preponderant over the variation of soil water content at specific potentials, especially those related to permanent wilting point.

Regarding OM content, a mean value of 3.649 dag kg−1 was observed for the Ultisol and 2.554 dag kg−1 for the Oxisol (Table 3). The maximum values indicated the existence of sites with a high decomposition capacity and stability of organic residues (3.087 and 7.240 dag kg−1). The highest OM variability was observed for the Ultisol (42.35%).

Soil water content at equivalent tensions θFC and θPWP presented mean values of 0.285 and 0.160 m3 m−3 for the Oxisol and 0.210 and 0.160 m3 m−3 for the Ultisol, respectively (Table 3). Despite the amplitude of CL contents, θPWP values of both soils were very close. Klein et al. (2013) reported that θPWP is also related to intra-aggregate pores, with BD being the preponderant factor in the amount of cryptopores in soils. The structural units of aggregates are disrupted as BD increases, leading to an increase in textural pores, responsible for water retention at potentials lower than −15000 hPa. In addition, clay increases the specific surface area of the soil matrix, and capillarity and adsorption phenomena determine the matric potential, responsible for soil water retention (Létourneau et al., 2015). Based on these observations, clay content and soil compaction (represented by BD) in these systems may have governed soil water retention conditions, especially in relation to potentials equivalent to θPWP.

The Shapiro & Wilk test confirmed the normal distribution for the attributes CL, SD, and θFC (Table 3). Although it was significant for the other attributes, indicating deviations from normality, the classifications were considered as distribution tending to normality since the mean values were close to the median.

Tables 1 and 2 show the pedofunctions used to estimate soil water contents at specific potentials, theoretically θFC and θPWP. Their respective coefficients of determination showed the quality of model adjustments, with R2 higher than 0.90 for most cases and all of them significant at 1% probability. A moderate to high correlation was verified between the observed and estimated θFC data (R > 0.74), with a small tendency to overestimate values above 0.30 m3 m−3 and underestimate values below 0.20 m3 m−3 (Figure 2). Although the residuals of pedofunctions generated with soil data from Brazil (Arruda et al., 1987; van den Berg et al., 1987; Oliveira et al., 2002) were higher when compared to the other models, they presented a good performance even without taking into account attributes inherent to edaphology and soil compaction (i.e., OM and BD).

FIGURE 2 Linear regressions between observed and estimated θFC values obtained from the proposed models. 

Contrary to what was observed in this study, Bonilla & Cancino (2001) observed a low accuracy for Chilean soils. This limitation was overcome by working on a large database to allow a division of soils into more homogeneous classes. According to Reichert et al. (2009), point scattering is higher and water retention accuracy is lower when using pedofunctions generated from a database with characteristics that differ considerably from soils where the model is assessed. Pedofunctions will only efficiently express water retention of soils with genesis and mineralogy similar to that of the database that was generated (Mecke et al., 2002).

The estimates of θPWP presented lower point scattering and higher accuracy of models when compared to θFC (Figure 3). All tested functions were close to the 1:1 line on a 45° slope, except for the functions of Ritchie et al. (1999) and Silva et al. (1994). This behavior reflected a high correlation of estimates with the observed data due to an R2 higher than 0.90. In addition, the results showed that changes imposed on the Oxisol by agriculture led to an increase in water volume retained at potentials lower than −15000 hPa, in which θPWP values were higher than 0.16 m3 m−3 in most cases, even in integrated production systems. The estimates of θPWP allowed a more detailed observation of the Oxisol database, in which OM and BD contents were not significant in the pedofunctions of Gupta & Larson (1979), van den Berg et al. (1987), and Oliveira et al. (2002) (Table 2). On the other hand, OM and BD contents were significant in the adjustment of θPWP functions for the Ultisol. According to Rawls et al. (2003), the use of contents of soil organic carbon and their particle size distribution as predictors leads to a small improvement in water content predictions related to the matric potential of −15000 hPa when compared to functions that use only particle size distribution as predictors.

FIGURE 3 Linear regressions between observed and estimated θPWP values obtained from the proposed models. 

Bonetti et al. (2017) studied the water retention of an Oxisol and Ultisol under integrated crop-livestock systems (ICL) and verified that changes imposed by the management system on soil porosity modified θFC to a higher degree when compared to θPWP. The adequate animal stocking rate and dwell time of the forage crop in ICL can favor the reorganization of porous space by the root system development. This strategy contributes to increasing the water content available to plants, with direct changes in microporosity (Bonetti et al., 2017). In this sense, the management system adopted for the Oxisol (ICL with an intensive crop rotation and high animal stocking rate) may not have been adequate to the maintenance of a pore structure with a diameter lower than 0.2 μm, which favored micropore disruption, directly reinforcing the effect of clay contents under soil compaction conditions. In this case, the function adjustment procedure itself is responsible for maintaining or excluding a certain attribute, aiming at the adequacy of adjustment coefficients, as well as the errors between the generated output patterns to reach the desired minimum value, i.e., close to zero.

As in R2, ANN showed higher efficiency in the estimation of θFC and θPWP. ANN, Arruda et al. (1987), and van den Berg et al. (1987) were the best classified for the MSE, RMSE, and MAPE values of the pedofunctions that estimated θFC (Table 4). On the other hand, ANN, Rawls et al. (1982), and van den Berg et al. (1987), in this order, were the best for those that estimated θPWP. MSE was a sensitive evaluator to errors of pedofunctions because it raised the individual differences between the observed and estimated squared values. This evaluator is always positive and, when zero, indicates the perfect model simulation. In addition to MSE, RMSE also expresses the accuracy of results, with error values under the same dimensions of the analyzed variable. MAPE is a less robust evaluator and showed the error representativeness in relation to the total of the measured observations. In this case, ANNs were classified first in the pedofunctions rank, with lower MSE, RMSE, and MAPE in both θFC and θPWP estimates.

TABLE 4 Mean square error (MSE), root mean square error (RMSE), and mean absolute percentage error (MAPE) calculated from the proposed θFC and θPWP pedofunctions. 

Fonte θFC θPWP


MSE RMSE MAPE Rank1 MSE RMSE MAPE Rank1
Oxisol
Silva et al. (1994) 0.0004 0.0220 0.0118 6th 1.54×10-5 0.0039 0.0075 5th
Gupta & Larson (1979) 0.0005 0.0228 0.0485 7th 0.0001 0.0114 0.0694 6th
Rawls et al. (1982) 0.0004 0.0202 0.0184 5th 9.08×10-6 0.0030 0.0029 2nd
Saxton et al. (1986) 0.0009 0.0304 0.0189 8th - - - -
Ritchie et al. (1999) 0.0826 0.2875 0.0046 9th 0.0001 0.0135 0.0103 8th
Arruda et al. (1987) 0.0003 0.0192 0.0021 2nd 1.17×10-5 0.0034 0.0004 4th
van den Berg et al. (1987) 0.0003 0.0193 0.0119 3rd 9.08×10-6 0.0030 0.0029 3rd
Oliveira et al. (2002) 0.0003 0.0194 0.0012 4th 0.0001 0.0114 0.0694 7th
Artificial neural network 0.0002 0.0142 0.0018 1st 5.22×10-6 0.0022 0.0019 1st
Ultisol
Silva et al. (1994) 0.0016 0.0411 0.0424 7th 0.0036 0.0601 0.3087 8th
Gupta & Larson (1979) 0.0004 0.0222 0.0338 2nd 3.73×10-5 0.0061 0.0121 2nd
Rawls et al. (1982) 0.0006 0.0256 0.0654 4th 0.0002 0.0146 0.0137 3rd
Saxton et al. (1986) 0.0012 0.0359 0.0587 6th - - - -
Ritchie et al. (1999) 0.0080 0.0895 0.3519 8th 0.0006 0.0254 0.0371 6th
Arruda et al. (1987) 0.0005 0.0229 0.0588 3rd 0.0002 0.0151 0.0170 4th
van den Berg et al. (1987) - - - - 0.0002 0.0151 0.0170 5th
Oliveira et al. (2002) 0.0012 0.0357 0.0989 5th 0.0008 0.0291 0.0915 7th
Artificial neural network 4.94×10-6 0.0022 0.0043 1st 6.56×10-6 0.0025 0.0096 1st

1 Rank: classification based in lower MSE, RMSE and MAPE.

The estimates generated by these two adjustment categories could be considered as satisfactory and valid, but the use of multiple linear regression models to predict θFC values below 0.20 m3 m−3 may present a slight tendency to overestimate it, which was not observed by the neural network. The pedofunctions applied to LLWR showed that the available soil water content (AW), represented by the difference between θFC and θPWP, was positively influenced by an increase in BD between 0.69 and 1.06 Mg m−3 in all cases (Figure 4C, D). This behavior confirms the positive relationship between soil compaction and the available water range (without considering restrictions imposed by θPR), in which the water content retained at potentials of −100 and −15000 hPa is higher. The models proposed by Silva et al. (1994) and Ritchie et al. (1999) stood out from the other pedofunctions in both soils, indicating an excess LLWR of 0.02 m3 m−3 in the Oxisol (Figure 4A) and a deficit of 0.04 m3 m−3 in the Ultisol (Figure 4B) based on the estimates carried out by ANN, which had the best performance in both soils.

FIGURE 4 Variation of LLWR in the Oxisol (A) and Ultisol (B) and available water content in the Oxisol (C) and Ultisol (D) using the tested pedofunctions. 

Regarding the critical BD, in which LLWR is zero, all the proposed models for Oxisol showed LLWR zero for a BD of 1.33 Mg m−3, while most of the models for the Ultisol presented LLWR zero for a BD of 1.38 Mg m−3 (Figure 4A, B). In this case, the models of Oliveira et al. (2002) and Ritchie et al. (1999) underestimated and overestimated the critical BD in the Ultisol, respectively. For LLWR construction in the Ultisol using the pedofunctions proposed by Oliveira et al. (2002), the critical BD would be 1.35 Mg m−3, while using the pedofunctions proposed by Ritchie et al. (1999), the critical BD would be 1.61 Mg m−3 (Figure 4B). Considering that LLWR accesses soil physical quality through BD, the main objective of its determination is to clarify the critical BD so that preventive actions are taken in agricultural systems. In the evaluated systems, the θPR curve was the preponderant factor in the establishment of the critical BD.

Regardless of the pedofunctions used for LLWR construction in the Oxisol, it was not restricted by the air-filled capacity curve (θAFC) (Figure 5). The θAFC was above θFC in all cases, not being a preponderant factor even at high BD levels. According to Gubiani et al. (2013), there are practically no criticisms reported in the Brazilian literature for the upper LLWR limits. Most crops are grown on soils with optimum drainage, where the period of water excess, i.e., soil aeration deficiency is much lower when compared to periods of water deficit. Under these soil conditions, studies have indicated a higher relationship of plant development with PR (Freddi et al., 2009; Kaiser et al., 2009), being more frequent than with θAFC.

FIGURE 5 LLWR construction of the Oxisol as a function of soil bulk density using the proposed pedofunctions to estimate θFC and θPWP. 

When the proposed pedofunctions are used to construct the LLWR concept, it is evident that the main changes occur on the available soil water content (AW). In the Oxisol, LLWRs estimated by ANN, Gupta & Larson (1979), Rawls et al. (1982), Ritchie et al. (1999), Arruda et al. (1987), Oliveira et al. (2002), and van den Berg et al. (1987) were similar (Figure 5). The model presented by Silva et al. (1994) overestimated AW values for conditions of lower bulk density, i.e., between 0.75 and 1.2 Mg m−3 (Figure 5B). In contrast, the model of Ritchie et al. (1999) underestimated AW at low BD levels and then presented significant AW gains with an increase in BD (Figure 5E).

Considering the results obtained for the Ultisol, it was evident that AW was overestimated under all BD conditions when the pedofunctions proposed by Silva et al. (1994) were used (Figure 6B). The model proposed by Ritchie et al. (1999), as observed for the Oxisol, underestimated AW at low BD levels and overestimated AW at high BD levels, which would restrict its use for this type of soil (Figure 6E).

FIGURE 6 LLWR construction of the Ultisol as a function of soil bulk density using the proposed pedofunctions to estimate θFC and θPWP. 

The results obtained in this study provided important information for the management of compacted and/or irrigated areas, demonstrating the use of the main models to estimate θFC and θPWP, the result on LLWR determination, and available water of two soils frequently found in Brazil. In addition, further studies using a larger database are needed, allowing the establishment of an artificial neural network that could be validated for Brazilian soils or tropical regions.

CONCLUSIONS

Among the evaluated pedofunctions, multilayer perceptron artificial neural networks are more efficient to estimate water contents in the field capacity and permanent wilting point.

Pedofunctions that use contents of sand, clay, organic matter, and soil bulk density are more efficient in estimating water contents in the field capacity and permanent wilting point.

Multiple linear regression techniques are inferior regarding statistics that measure the accuracy of models and tend to overestimate water content values in the field capacity.

Pedofunctions differ in the establishment of the critical bulk density when they are used to calculate the least limiting water range, exposing the limitations of the models.

ACKNOWLEDGMENTS

To the Coordination for the Improvement of Higher Education Personnel (CAPES) for granting the scholarship to the first author. To Embrapa Agrosilvopastoral and Certeza Farm for providing one of the areas for study.

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Received: January 19, 2018; Accepted: May 29, 2019

1*Corresponding author. Universidade Estadual Paulista "Júlio de Mesquita Filho" - UNESP/ Ilha Solteira - SP, Brasil. E-mail: renan.tavanti91@gmail.com

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