ABSTRACT

Soil is a medium that stores and transfers air, water, nutrients and heat to microorganisms and plants. Its water storage capacity is studied by analysing water retention curves (WRCs), which establish the relationship between soil water content and the force with which water is retained. The objective of this work was to evaluate the capacity of functional geostatistics in predicting the spatial distribution of water retention curves in two types of soils. Experimental areas with two types of soil, Andisol and Oxisol, were selected, and a regular grid of 75 sites was established, from which water retention curves were obtained at two depths. The curves were subjected to geostatistical functional analysis (GF), and the applicability of this method was evaluated by obtaining the usable water table (LAA) and comparing the results with experimental data obtained using traditional methods. Based on cross-validation, it was verified that GF produced a better fit for the Andisol since the coefficient of determination between the LAA values for the measured data and predictions was high, with an R² of 99%; however, the proposed methodology was also reliable for the Oxisol, since an R² of 94% was obtained at the two depths studied.

Key words:
usable water; spatial variability; functional data; functional kriging

RESUMO

O solo é um sistema que armazena e transfere ar, água, nutrientes e calor para microrganismos e plantas. Sua capacidade de armazenamento de água é estudada analisando a curva de retenção de água (WRC), que estabelece a relação entre a umidade do solo e a força com que ela é retida. O objetivo deste trabalho foi avaliar a capacidade preditiva da geoestatística funcional na distribuição espacial das curvas de retenção de água em dois tipos de solos. Foram selecionadas duas áreas experimentais, um Andisol e um Oxisol, nas quais foi estabelecida uma grade regular com 75 pontos, das quais foram obtidas curvas de retenção de água em duas profundidades. As curvas foram submetidas à análise geoestatística funcional (GF), sua aplicabilidade foi avaliada obtendo a tabela de água utilizável (LAA) e sua posterior análise espacial por métodos tradicionais nos quais os resultados foram comparados com os dados experimentais. Com base na validação cruzada, verificou-se que o uso de GF tem um melhor ajuste para o Andossolo, uma vez que o coeficiente de determinação entre os valores de LAA obtidos com os dados observados e aqueles obtidos com as previsões foi alto, com R² de 99%; no entanto, para o Latossolo, a metodologia proposta também é confiável, uma vez que foi obtido um R² de 94% nas duas profundidades estudadas.

Palavras-chave:
variabilidade espacial; água útil; dados funcionais; kriging funcional

HIGHLIGHTS:

Elevated compaction and the micropores flattened retention curves.

Slight field capacity - permanent wilting point differencev.

Ground-based data (GF) demonstrate excellent accuracy for Andisols and for Oxisols at different depths.

Introduction

Agricultural soils behave as complex systems that store and transport air, water, nutrients, and heat to microorganisms and plants (Kaur et al., 2021Kaur, T.; Devi, R.; Kour, D.; Kour, D.; Yadav, A.; Yadav, A.N.; Dikilitas, M.; Abdel-Azeem, A.; Ahluwalia, A.; Saxena, A. Plant growth promoting soil microbiomes and their potential implications for agricultural and environmental sustainability. Biologia, v.76, p.2687-2709, 2021. https://doi.org/10.1007/s11756-021-00806-w
https://doi.org/10.1007/s11756-021-00806... ). Porosity plays an important role in a soil’s water storage capacity because the presence of small water-filled pores require plants to exert greater force to extract the water (Howe & Peyton-Smith, 2021Howe, J. A.; Peyton-Smith, A. The soil habitat. In: Gentry, T. J.; Fuhrmann, J. J.; Zuberer, D. A. Principles and Applications of Soil Microbiology, Elsevier, 2021, Cap.2, p.23-55.).

Studies of soil water retention curves (WRCs) establish links between stored water and the force that is needed to retain it. Commonly studied critical soil water contents include field capacity (FC), which is measured after the soil has lost water due to gravity, and the permanent wilting point (PWP), which occurs after plants have already taken in available water and cannot absorb more water from the soil.

Recently, several studies have been conducted that employed alternative methods for performing spatial analysis through which spatial predictions can be made at each measurement site that has a known curve but no specific data points (Sajedi-Hosseini et al., 2018Sajedi‐Hosseini, F.; Choubin, B.; Solaimani, K.; Cerdà, A.; Kavian, A. Spatial prediction of soil erosion susceptibility using a fuzzy analytical network process: Application of the fuzzy decision making trial and evaluation laboratory approach. Land degradation & development, v.29, p.3092-3103, 2018. https://doi.org/10.1002/ldr.3058
https://doi.org/10.1002/ldr.3058... ; Chen et al., 2019Chen, W.; Panahi, M.; Khosravi, K.; Pourghasemi, H. R.; Rezaie, F.; Parvinnezhad, D. Spatial prediction of groundwater potentiality using ANFIS ensembled with teaching-learning-based and biogeography-based optimization. Journal of Hydrology, v.572, p.435-448, 2019. https://doi.org/10.1016/j.jhydrol.2019.03.013
https://doi.org/10.1016/j.jhydrol.2019.0... ; Padarian et al., 2022Padarian, J.; Stockmann, U.; Minasny, B.; McBratney, A. Monitoring changes in global soil organic carbon stocks from space. Remote Sensing of Environment, v.281, p.113260, 2022. https://doi.org/10.1016/j.rse.2022.113260
https://doi.org/10.1016/j.rse.2022.11326... ). These methods, known as functional geostatistics (GF) (Mateu & Giraldo, 2022Mateu, J.; Giraldo, R. Introduction to Geostatistical Functional Data Analysis. In: Mateu, J.; Giraldo, R. Geostatistical Functional Data Analysis. Wiley Series in Probability and Statistics. 2022. Cap.1, p.1-25.), require the application of smoothing techniques to convert the discrete data from each site into continuous functions. Using GF analysis, it is possible to perform spatial interpolation on these curves.

In this study, GF was applied to WRCs to obtain usable water contents to evaluate the predicative capacity of GF and its potential use as a tool for describing the spatial variability in WRCs. Next, a cross-validation analysis was performed (using sites where data were already measured) to estimate prediction errors and compare them with the traditional univariate prediction methods that are often used for spatial analysis. Thus, the objective of this work was to evaluate the predictive capacity of functional geostatistics and its potential as a tool for describing the spatial variability in water retention curves in two types of soils.

Materials and Methods

Two experimental locations were selected for this study. The first is in the municipality of Mosquera (Cundinamarca) at geographical coordinates of 4° 42’ N and 74° 12’ W, with an altitude of 2,543 m.a.s.l. The average mean temperature at this site is 13.1 °C, and the average annual precipitation is 670 mm. The site is part of the Bogotá River basin, which contains soil from the Marengo series, and the soil is classified as a Typic Melanudand with silty-loam and clay-loam textures and slopes of less than 1%. The soil is an Andisol with a thick, dark Ap horizon that originates from lake sediments with a small amount of volcanic ash and is supported by alluvial clay characterized by naturally poor and incomplete drainage, salinity problems, and low sodium contents. The experimental unit was 3.1 ha^-1 and was used for crops and grazing activities (Figure 1A).

The second sampling zone was located in the municipality of Puerto López, Meta, Colombia (4° 22’ 38.50” N and 72° 13’ 24.53” W, with an altitude of 156 m.a.s.l). Precipitation in this zone follows a monomodal regime with an annual average of 2,375 mm; the mean temperature is 27 °C, and the relative humidity is 75% (Jaimes et al., 2003Jaimes, W.; Navas, G.; Salamanca, C.; Conde, A. Estudio detallado de suelos de la estación experimental de Corpoica “Sabanas” en la Altillanura Colombiana. Corpoica, C. I. La Libertad, Villavicencio, Colombia, v.62, p.1-9, 2003.). The most predominant soil in this zone is a Typic Haplustox, which contains a thick layer of topsoil with a fine, loamy, silty texture and a slightly inclined slope (<5%). This soil is susceptible to physical degradation due to extensive ranching activities on the native meadows. The experimental unit covered 37 ha and was used for growing corn during the sampling period (Figure 1B).

In both zones, sampling was performed at two depths (0 to 10 cm and 10 to 20 cm) by using an evenly spaced grid with 75 measurement locations. To determine the soil water retention curves at each sampling site, membrane equipment and pressure cookers were used at pressures of 0.1, 0.3, 0.5, 1, 3, 5, 10, and 15 bar, as well as at the saturation point (0 bar). In addition, soil water content was determined at each pressure. The mean curve was determined for each depth and the two soil types, and the differences between the values of the WRC at each measurement site and the averages of these values were calculated to obtain an “error curve” for each site. In addition, soil water retention was evaluated at the study sites by using the mean WRCs obtained at each depth.

B-splines (Zheng & Chen, 2022Zheng, Y.; Chen, F. Volumetric parameterization with truncated hierarchical B-splines for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering, v.401, p.1-19, 2022. https://doi.org/10.1016/j.cma.2022.115662
https://doi.org/10.1016/j.cma.2022.11566... ) were used in this study to estimate the error curves at each of the 75 measurement sites. Next, these curves were subjected to functional kriging (Mateu & Giraldo, 2022Mateu, J.; Giraldo, R. Introduction to Geostatistical Functional Data Analysis. In: Mateu, J.; Giraldo, R. Geostatistical Functional Data Analysis. Wiley Series in Probability and Statistics. 2022. Cap.1, p.1-25.) by removing one error curve at a time and performing functional kriging on the remaining 74 curves to predict the “missing” curve, which resulted in the “observed” curve (estimated using B-splines) and the predicted curve for the unmeasured site (using functional kriging). The WRC was calculated at each site by fitting the calculated average curve with a correction from the “error” curve that was predicted at each site. A group of 75 measured WRCs and 75 predicted WRCs was generated, which allowed (leave-one-out) for cross-validation analysis to be performed. This procedure is useful for evaluating the quality of a method (the smaller the difference between the estimations and predictions, the better the method) and for comparing this method with traditional alternatives.

The functional kriging predictor is defined as follows (Giraldo et al., 2010Giraldo, R.; Delicado, P.; Mateu, J. Continuous time-varying Kriging for spatial prediction of functional data: an environmental application, Journal of Agricultural, Biological, and Environmental Statistics v.15, p.66-82, 2010. https://doi.org/10.1007/s13253-009-0012-z
https://doi.org/10.1007/s13253-009-0012-... ):

where χ(s₀) is the predicted curve at site s₀, χ(s_i) corresponds to the curve observed at site s_i, and i = 1.2, …, n and λ_i, i = 1, …, n, are the weighting parameters that indicate the contributions of each observed curve to the predicted curve.

The λ_i parameters are estimated by solving the following system of equations (Giraldo et al., 2010Giraldo, R.; Delicado, P.; Mateu, J. Continuous time-varying Kriging for spatial prediction of functional data: an environmental application, Journal of Agricultural, Biological, and Environmental Statistics v.15, p.66-82, 2010. https://doi.org/10.1007/s13253-009-0012-z
https://doi.org/10.1007/s13253-009-0012-... ):

where the integrals correspond to the trace-variogram function (Giraldo et al., 2010Giraldo, R.; Delicado, P.; Mateu, J. Continuous time-varying Kriging for spatial prediction of functional data: an environmental application, Journal of Agricultural, Biological, and Environmental Statistics v.15, p.66-82, 2010. https://doi.org/10.1007/s13253-009-0012-z
https://doi.org/10.1007/s13253-009-0012-... ) evaluated for the distances between the observation sites (matrix to the left of the equal sign) and the distances between the observation sites and the prediction site (vector to the right of the equal sign). These integrals are calculated by estimating the trace-variogram function that is given by the following expression (Giraldo et al., 2010):

where N(h) = {(s_i, s_j):||s_i - s_j|| = h} corresponds to the number of pairs of sites separated by hours and its subsequent fit with traditional parametric semivariance models (spherical, exponential, Gaussian, Matérn).

Using the measured curves and those obtained using functional prediction, available water content (AWC) was calculated at each site and for each soil. AWC was defined as the difference between the water contents at the FC and PWP at pressures of 0.3 and 15 bar, respectively (Melián et al., 2023Melián, E.; Gatica, G.; Pucheta, E. Compromisos de rasgos del leño en plantas del desierto: un modelo triangular para comprender las variaciones intra e interespecíficas a lo largo de un gradiente de aridez. Austral Ecology, v.1, p.1-16, 2023. https://doi.org/10.1111/aec.13370
https://doi.org/10.1111/aec.13370... ).

The results obtained from functional kriging were compared with those obtained using univariate kriging at two depths. To perform a conventional analysis, the semivariance function was calculated for values of AWC and according to Cressie (1993Cressie, N. Statistics for spatial data. 1ed.; John Wiley & Sons, Inc., Wiley Series in Probability and Statistics, 1993. https://doi.org/10.1002/9781119115151
https://doi.org/10.1002/9781119115151... ), as follows:

where z(x_i) is the value of the LAA at point x_i, z(x_i + h) is the value of LAA at a point with a distance of h from the previous point, and N(h) is the number of pairs of data separated by the distance h. Next, this semivariogram is fit using one of the theoretical semivariance models mentioned earlier. Various criteria are considered for selecting the best model, including the coefficient of determination (R²), the least sum of squared errors (LSSE) and the cross-validation correlation (CVC). The shared parameters among the theoretical semivariance models include the nugget (C0), which is a discontinuity in the semivariogram at the origin, the variance of the process (C), and the reach (r), which is the distance to a spatial correlation. In addition, the nugget-variance ratio, C/(C0+C), is often used as a criterion for model selection. This parameter establishes the degree of spatial dependence (DSD) expressed by the attribute under study. Cambardella et al. (1994Cambardella, C. A.; Moorman, T.B.; Novak, J. M.; Parkin, T.B.; Karlen, D. L.; Turco, R. F.; Konopka, A. E. Field-scale variability of soil properties in Central Iowa Soils, Soil Science Society of America Journal, v.58, p.1501-1511, 1994. https://doi.org/10.2136/sssaj1994.03615995005800050033x
https://doi.org/10.2136/sssaj1994.036159... ) state that the dependence is strong if the DSD is greater than 75%, is moderate for values between 25 and 75%, and is weak for values less than 25%. For all estimations and data processing, R version 4 was used with the libraries Geofd, fda and geoR.

Results and Discussion

Figure 2 shows that in both cases, the soil demonstrated flat WRCs with similar behaviours at each studied depth and small differences between the FC and PWP, which indicated the presence of a large number of micropores and that soil compaction occurred (Villalobos-Baquero & Meza-Montoya, 2019Villalobos-Barquero, V.; Meza-Montoya, A. Impacto en la densidad aparente del suelo provocado por el tránsito de búfalos (Bubalus bubalis) en arrastre de madera. Revista de Ciencias Ambientales, v.53, p.147-155, 2019. https://dx.doi.org/10.15359/rca.53-2.8
https://dx.doi.org/10.15359/rca.53-2.8... ).

The curves obtained in both types of soil are common among loamy soils according to the findings of Tarazona-Meza et al. (2022Tarazona-Meza, N.; Chavarría-Párraga, J.; Moreira-Saltos, J. El cultivo de maíz y sus necesidades hídricas en Manabí, Ecuador. Revista de Ciencias Agropecuarias ALLPA, v.5, p.2-11, 2022. https://publicacionescd.uleam.edu.ec/index.php/allpa/article/view/349
https://publicacionescd.uleam.edu.ec/ind... ), who observed FC and PWP values of 0.23 cm³ cm^-3 and 0.19 cm³ cm^-3 in an Oxisol and 0.30 cm³ cm^-3 and 0.26 cm³ cm^-3 in an Andisol at both depth ranges. In addition, these values were similar to those reported by Vargas-Díaz et al. (2022Vargas Diaz, R. E.; Wilches Ortiz, W. A.; Espitia Malagón, E. M. Efecto del establecimiento de sistemas de rotación para el cultivo de la papa sobre las características químicas y físicas del suelo. Siembra, v.9, p.1-9, 2022. https://doi.org/10.29166/siembra.v9i2.4023
https://doi.org/10.29166/siembra.v9i2.40... ), Zhang et al. (2020Zhang, X.; Wendroth, O.; Matocha, C.; Zhu, J.; Reyes, J. Assessing field-scale variability of soil hydraulic conductivity at and near saturation. Catena, v.187, p.1-11, 2020. https://doi.org/10.1016/j.catena.2019.104335
https://doi.org/10.1016/j.catena.2019.10... ) and Gómez-Rodríguez et al. (2013Gómez-Rodríguez, K.; Camacho-Tamayo, J. H.; Vélez-Sánchez, J. E.; Changes in water availability in the soil due to tractor traffic. Engenharia Agricola, v.33, p.1156-1164, 2013.).

The increased prevalence of clays in the Andisol signifies an increased presence of micropores, as documented in this region by Varón-Ramírez et al. (2018Varón-Ramírez, V.M.; Camacho-Tamayo, J.H.; González-Nivia, J. Management zones determination based on physical properties of the soil. Ciência & Agrotecnologia, v.42, p.248-260, 2018. http://dx.doi.org/10.1590/1413-70542018423002318
http://dx.doi.org/10.1590/1413-705420184... ). Consequently, a close arrangement of solid particles and a reduced prevalence of macropores are evident in the Andisol compared to the Oxisol. This results in more pronounced capillarity in the Andisol, leading to enhanced interactions with water. This, in turn, results in a predominance of water retention over water drainage at lower tensions, as observed in the research conducted by Silva et al. (2022Silva, F. G.; De Assis Junior, R. N.; Shiso Toma, R.; De Sousa Oliveira, L.; Da Silva Marques, E.; Anunciato Mota, J. C. Physical-hydraulic attributes as indicators of functionality of soil pores under different compaction levels. Revista Caatinga, v.35, p.884-893, 2022. https://doi.org/10.1590/1983-21252022v35n416rc
https://doi.org/10.1590/1983-21252022v35... ). This phenomenon leads to greater water storage capacity, as depicted in the obtained curves.

The WRCs obtained for both soils do not follow general trends, which demonstrates a lack of homogeneity in the data (Figure 3). Thus, within the study zones, the water retention behaviours at some sites are noticeably different from the rest. Nevertheless, the curves show the same asymptotic patterns in the desaturation zones with respect to FC.

To understand the behaviour of the study zones more clearly, descriptive measures for FC and PWP were calculated (Table 1). In both soils, the WRCs behaved similarly at both depths with respect to these measures. As seen in Figure 3, for the Andisol, the FC varied between approximately 0.13 cm³ cm^-3 and 0.55 cm³ cm^-3, and in the Oxisol, the FC varied between approximately 0.06 cm³ cm^-3 and 0.40 cm³ cm^-3. The difference between the FC and PWP was greater in the Andisol, indicating greater water availability in the soil in the study area.

Overall, the water contents at FC and the PWP showed mean variability at both depths, with CVs between 12 and 60%. This finding corresponded with the findings of Warrick & Nielsen (1980Warrick, A. W.; Nielsen, D. R. Spatial variability of soil physical proprieties in field, HILLEI, D. Applications of soil physics, Academic Press, 1980.) and could be attributed to the degree of disturbance that the soil has undergone.

WRC predictions were performed at the 75 measurement sites. The measured and predicted curves for the Andisols are shown in Figure 3, and those for the Oxisols are shown in Figure 4. In both cases, few differences were found between the two sets of curves.

Using measured data and predicted curves at each site, the available water content (AWC) was calculated as the difference between the water contents at FC and the PWP. This value served as a numerical indicator of the goodness-of-fit when a simple linear regression was performed to compare the measured and predicted values at each site. In addition, this value indicated which soil type was most suited for GF analysis to predict WRCs. The resulting regressions are shown in Figure 5. A strong correlation was observed between the observations and predictions. The coefficient of determination was higher in the Andisol (0.99) than in the Oxisol (0.94) at both depths. Despite the high R² value of the Oxisol, greater data scatter was observed. The values of R² indicated that more than 99% (Andisol) and 94% (Oxisol) of the measured data could be explained by the proposed predictor.

The model might have performed better for the Andisol because this soil has a higher content of organic matter and a higher clay content compared to the Oxisol. Organic matter content as well as clay content affects the pedotransfer functions and, as presented in this study, alters the water retention curves since organic matter and clays affect the presence and distribution of pores in the soil (Albuquerque et al., 2022Albuquerque, E.A.C.; de Faria Borges, L.P.; Brasil Cavalcante, A.L.; Lemos Machado, S. Prediction of soil water retention curve based on physical characterization parameters using machine learning. Soil and Rocks, v.45, e2022000222, 2022. http://doi.org/10.28927/SR.2022.000222
http://doi.org/10.28927/SR.2022.000222... ; Veloso et al., 2023Veloso, M. F.; Rodrigues, L. N.; Fernandes Filho, E. I.; Veloso, C. F.; Rezende, B. N. Pedotransfer functions for estimating the van Genuchten model parameters in the Cerrado biome. Revista Brasileira de Engenharia Agrícola e Ambiental, v.27, p.202-208, 2023. https://doi.org/10.1590/1807-1929/agriambi.v27n3p202-208
https://doi.org/10.1590/1807-1929/agriam... ).

The zones analysed in this study show high levels of compaction and an elevated presence of micropores, which were inferred from the trends and flattened shape of the soil water retention curves, with a small difference between FC and the PWP.

To evaluate the applicability of functional geostatistics in predicting data from water retention curves, geostatistical parameters were determined (Table 2), and spatial distribution maps were generated (Figures 6 and 7) for the values of AWC that were calculated using the measured data and the data obtained from the predictor.

For both soils and at both soil depths, the generated geostatistical parameters were similar, which demonstrated the goodness of fit of the functional predictor used in this study. The experimental and functional kriging-predicted AWC data fit the theoretical semivariogram models well, with the Andisol fitting the spherical models and the Oxisol fitting the exponential models at both depths.

At 0-10 cm in the Andisol, the AWC showed a moderate DSD, and the values of Co were relatively far from zero. At 10-20 cm in the Andisol and at both depths in the Oxisol, the Co values were much closer to zero, which indicated a strong spatial dependence that was also evidenced by DSD values above 75% (Birol & Günal, 2022Birol, M.; Günal, H. Field scale variability in soil properties and silage corn yield. Soil Studies, v.11, p.27-34, 2022. http://doi.org/10.21657/soilst.1143238
http://doi.org/10.21657/soilst.1143238... ). These results indicate that the sampling distances were adequate, since when greater distances between points exist, the variograms tend to present larger nugget due to the intrinsic properties of the soil, which also results in greater estimation errors when spatial pedotransfer functions are developed (Castrignano et al., 2023Castrignanò, A.; Heydari, L.; Bayat, H. Scale-dependent field partition based on water retention functional data. Land, v.12, p.1106, 2023. https://doi.org/10.3390/land12051106
https://doi.org/10.3390/land12051106... ), causing the sill to exceed the sampling variance, especially in areas that present different soil types as well as different levels of anthropogenic intervention (Camacho-Tamayo et al., 2008Camacho-Tamayo, J.H.; Luengas, C.A.; Leiva, F.R. Effect of agricultural intervention on the spatial variability of some soils chemical properties in the eastern plains of Colombia. Chilean journal of agricultural research. v.68, p.42-55, 2008.; Heydari et al., 2023Heydari, L.; Bayat, H.; Castrignanò, A. Scale-dependent geostatistical modelling of crop-soil relationships in view of Precision Agriculture. Precision Agriculture, v.24, p.1261-1287, 2023. https://doi.org/10.1007/s11119-023-09989-5
https://doi.org/10.1007/s11119-023-09989... ).

The maps show the high spatial variability found in the soil relative to the properties analysed (Figures 6 and 7). The maps created from the values generated using functional kriging are consistent with the measured data maps, which show a spatial distribution that is similar to that of the measured data based on the minimal differences between the two sets of maps. The Oxisol shows somewhat more notable differences between the maps, with a CVC of 0.94, which is lower than that obtained for the Andisol.

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