Fitting the van Genuchten model to the measured hydraulic parameters in soils of different genesis and texture at the regional scale**

. Soil hydraulic parameters are a key input for predicting soil water retention curves and water flow. The van Genuchten model is widely used to fit the van Genuchten hydraulic parameters including residual water content, saturated water content, a fitting parameter related to the inverse of the air entry pressure, and the shape parameter. This study aimed to show the interrelations of the soil hydraulic parameters on a large scale with both the inherent soil properties and the genetic type. The measured van Genuchten parameters originated from soil water retention curves determined in 100 pedons at 4 depths corresponding to the main soil diagnostic horizons. The results showed that the effect of soil texture on the van Genuchten hydraulic parameters was greater than that of the genetic soil type. The van Genuchten hydraulic parameters were in general significantly higher in fine-textured than coarse-textured soils. The vertical distribution of the hydraulic parameters was more discontinuous in fine-than in coarse-textured soils. The van Genuchten equation fits well to measured soil water retention (R 2 > 0.885) and thereby can predict the soil water retention curve for a variety of soils with acceptable uncertainty and improve soil water conservation on a large regional scale.

The SWRC and the saturated hydraulic conductivity are useful inputs for predicting hydraulic conductivity as a function of water matric potential K(ψ).(Fuentes et al., 2020;Lipiec et al., 2021;Wang et al., 2022).
The SWRC along with the K(ψ) curve are important hydrodynamic characteristics used for the description of water and solute movement through the surface and subsurface in saturated and unsaturated porous soil (Khlosi et al., 2016;Szymkiewicz et al., 2008;van Genuchten and Pachepsky, 2011).However, the measurement of SWRC is time-consuming and expensive, which restricts its application (van Looy et al., 2017).Therefore, approaches for estimation (modelling) of SWRC based on inherent soil properties such as particle size distribution, organic matter content, plasticity index, and particle density using pedotransfer functions (PTFs) (Bai et al., 2021;Rawls et al., 2001;Wang et al., 2021), neural network analyses (Minasny and McBratney, 2007), hyperspectral imaging (Krzyszczak et al., 2023), and the hierarchical Bayesian probabilistic model (Yang et al., 2015) are developed.The van Genuchten model (van Genuchten, 1980) is widely used to fit retention data (pairs of soil water content-soil water potential data) and extend measured values to the whole range of soil water content.The hydraulic parameters of the model equation include θ s , θ r , α, and n (AL-Kayssi, 2021; Du et al., 2024;Usowicz et al., 2011;Wösten et al., 1999).
Using a sequence of empirical equations, Tian et al. (2018Tian et al. ( , 2020) ) extended the van Genuchten model to explain the effects of temporal variations in soil bulk density on changes in SWRCs.Other newly developed approaches allow estimating vG parameters and SWRC from soil electrical conductivity (Fu et al., 2021), electrical resistivity (Lu et al., 2020), and soil thermal conductivity along with texture, bulk density, and field capacity (Liu et al., 2024).Recent results also indicate that the use of machine learning estimators has become an interesting tool to enhance the estimation of the soil water retention curve (SWRC) based on physical characterization parameters (Albuquerque et al., 2022).The vG parameters are related to each other.In a study conducted by Fu et al. (2021) the relation allowed estimating the parameter α from the other vG parameters.
Although the approaches to estimate vG model parameters and, subsequently, the SWRC have been advanced for several decades, the effect of large-scale heterogeneity with consideration of both the genetic type and texture of soils in different environmental conditions has rarely been considered (Fu et al., 2021).The heterogeneity in the soil texture can affect SWRC characteristics through the effect on pore size distribution, shape, and connectivity (Bondì et al., 2022;Bouma and Anderson, 1997) and the impact of soil genetic types through the natural self-organization of soil as a result of specific soil-forming processes (Costantini and Mocali, 2022;Świtoniak et al., 2022).
This study aimed to show the effect of varied soil characteristics on the van Genuchten model parameters and SWRCs in a range of soils.The RETC (retention curve computer code) program (van Genuchten et al., 1991) was used to fit vG model parameters to measured soil water retention data from a previous survey comprising 100 pedons (Paluszek, 2011;Usowicz, 2011).We hypothesized that the both soil genetic type and the soil texture affect the van Genuchten hydraulic parameters at the large regional scale.The pedons including the main horizons represented the following genetic soil types: Luvisols derived from weathering silt formations, loess, loams, and loamy sands, Mollic Gleysols derived from loess-like deposits, loams, and loamy sands, and Phaeozems derived from loess.The soils derived from loess are prone to degradation by water and wind erosion, while those derived from sands are susceptible to agricultural drought.The degradation and recovery of the soils can be mediated by features of a given soil type associated with the pedogenesis process.

MATERIALS AND METHODS
The research was carried out in the central and southeastern parts of Poland (traverse length of approximately 550 km) (Fig. 1). 100 soil pedons representing the following genetic types were analyzed:  : 16, 12, 12, 12, 12, 12, 8, and 16.Bulk and undisturbed soil samples (in 4 replicates) were taken from the depths of 5-15, 30-40, 55-65, and 80-90 cm in all the soils.The depths correspond to the following diagnostic horizons: Eet, Bt, BC or C in Luvisols; Aa, Bbr, AC, Cg or G in Mollic Gleysols (depending on the subtype), and A, ABbr, Bbr or AC, Cca in Phaeozem soils (depending on the subtype) (Paluszek, 2011).A total 1 600 samples (100 pedons × 4 depths/horizons × 4 replicates) were used.All the soils were under cultivated cropland.The ploughing tillage system is usually used in the study area.The important threats limiting crop productivity are agricultural drought susceptibility and water erosion in central and south-eastern Poland, respectively.
The sampling was done immediately after harvest.The bulk samples were used to determine the particle size distribution using the sieving and hydrometer method (Ostrowska et al., 1991) and soil organic carbon by dry combustion using the analyzer Vario Max CNS Elementar (Elementar, 2000).The data were collected within the project report "Criteria for assessing the physical condition of selected systematic units of arable soils" (Paluszek, 2011;Usowicz, 2011).Undisturbed soil in 100 cm 3 steel cylinders (5.0 cm height) was used to determine the soil water retention curve (SWRC) with pressure plates (Soil Moisture Equipment Corp., Santa Barbara CA, USA) according to Richards' method (Klute and Dirksen, 1986a).After saturation, the following suction was consecutively applied to establish soil water matric potentials (in hPa): 1, 10, 31, 98, 155, 309, 490, 1 554, 4 900, and 15 540 to obtain the SWRC.Saturated hydraulic conductivity was measured with the constant head method in soil samples of 100 cm 3 using a laboratory permeameter (Eijkelkamp Agrisearch Equipments, The Netherlands) (Klute and Dirksen, 1986b).
The measured SWRCs were fit to the van Genuchten equation (van Genuchten, 1980) to derive the soil water retention curve and the hydraulic parameters with the RETC (retention curve computer code) (van Genuchten et al., 1991).The van Genuchten equation is as follows: , where: θ s -saturated water content (cm 3 cm -3 ), θ r -residual water content (cm 3 cm -3 ), h -matric potential (-cm), αfitting parameter related to the inverse of the air entry pressure (cm -1 ), n -fitting parameter that determines the shape of the soil water retention curve (dimensionless).

Basic soil properties
The data in Table 1 show that the ranges of sand (2-0.05mm), silt (0.05-0.002 mm), and clay (<0.002 mm) contents in the studied soils were 12.7-77.4%,12.2-74.9%,and 4.6-20.0%,respectively.In general, lower contents of clay and higher contents of sand and silt were observed at the depth of 5-15 cm than at all the depths below.Based on the sand content, we divided the soils into two groups: (1) fine-textured soils, including Luvisols derived from silt formations, Mollic Gleysols derived from loess-like silt, and Luvisols and Phaeozems derived from loess (A-D) and (2) coarse-textured soils, including Luvisols derived from loams and sands and Mollic Gleysols derived from loams and sands (E-H).The sand contents in the first group and the second group of soils ranged from 12 to 40% and from 60 to 78%, respectively, at all depths.According to Hengl et al. (2017) and Huang and Hartemink (2020), the second group can be classified as sandy soils (sand content >50% and clay content <20%).
The bulk density (BD) of the soils varied from 1.36 to 1.74 Mg m -3 depending on the soil type and depth (Table 1).In general, the lowest BD values were recorded at the depth of 5-15 cm within the plough layer (1.36-1.55Mg m -3 ) and increased in deeper soil correspondingly to the plough pan and/or the parent material (1.39-1.74Mg m -3 ).Irrespective of the soil type, the densities were higher in the sandier soils associated in part with greater content of sand with high particle density.
The saturated hydraulic conductivity (Ksat) varied from 22.5 to 248.5 cm day -1 depending on the soil type and depth (Table 1).The Ksat values in most soils (B, C, F, G, H) were higher at the depth of 5-15 cm within the plough layer and appreciably lower at all three depths below.In the case of Phaeozems (D) and Luvisols derived from loams (E), the highest Ksat (72.8 and 114.5 cm day -1 ) was noted at 55-65 or 80-90 cm, and the lowest values were recorded at 30-40 cm.The lowest Ksat at the depth of 30-40 cm within the plough pan of the D and E soils corresponded with the higher bulk densities (1.423 and 1.712 Mg m -3 ) than at the other depths in the pedon.The lowest differentiation of Ksat between the depths was recorded in Luvisols derived from silt formation (A): from 22.5 to 33.8 cm day -1 , and the largest range was noted in Luvisols derived from sands (G): from 108.6 to 401.4 cm day -1 .

Luvisols developed from silt formations (A)
Table 2 demonstrates that the residual water content (θ r ) varied from 0.0327 cm 3 cm -3 at the 30-40 cm depth to 0.0611 cm 3 cm -3 at 80-90 cm.The values of θ s , negative pressure heads at which air starts entering the soil matrix (1/α) (α = scaling parameter), and shape parameters (n) in the soil pedon had a parabolic shape with the lowest values at 55-65 cm (0.388 cm 3 cm -3 , 155.2 cm, and 1.396, respectively), and the highest values were obtained at 5-15 cm (0.417 cm 3 cm -3 , 301.1 cm, and 1.733, respectively).This similar distribution implies an existing positive relationship between the three vG parameters.The differences in all the vG parameters values between the depths were in most cases not significant (p<0.05)except the higher values of 1/α and n at 5-15 cm vs. 55-65 cm.

Mollic Gleysols developed from loess-like silt formations (B)
As can be seen from Table 2, θ r increased from 0.0027 cm 3 cm -3 at 5-15 cm to 0.0115-0.0172cm 3 cm -3 at all the deeper layers, while θ s decreased from 0.439 at the top 5-15 cm to 0.407 cm 3 cm -3 at 80-90 cm.Both 1/α and n had the lowest value at the 5-15 cm depth (87.13 cm and 1.255, respectively) and increased in the deeper soil to 175 cm and 1.493 at the 80-90 cm depth.The differences in all the vG parameters values between the depths were not significant (p<0.05).

Luvisols developed from loess (C)
The θ r had the lowest value at the top three upper layers (0.0211-0.0301 cm 3 cm -3 ) and increased to 0.0513 cm 3 cm -3 at the 80-90 cm depth (Table 2).θ s was similar in all four depths (0.399 to 0.421 cm 3 cm -3 ).The course of 1/α and n in the soil profile was similar, with the highest values at the 80-90 cm depth (372.52 cm and 1.840, respectively) and the lowest values at 55-65 cm (208.79 cm and 1.412, respectively).The θ r , 1/α, and n values were significantly (p<0.05)lower at 55-65 vs. 80-90 cm.

Phaeozems developed from loess (D)
The lowest θ r value (0.0123 cm 3 cm -3 ) was recorded at 55-65 cm, and the highest value of this parameter (0.0419 cm 3 cm -3 ) was noted at 80-90 cm (Table 2).The θ s values were similar at all the depths and varied from 0.417 to 0.451.1/α Ta b l e 2. Means (n=4) of the van Genuchten parameters including residual water content (θ r ), saturated water content (θ s ), matric water potentials at which air starts entering the soil (1/α where α is a fitting parameter related to the inverse of the air entry potential, fitting parameter that determine the shape of the soil water retention curve (n).Different letters indicate a significant difference between depths within the same soil by the LSD test (p<0.05)

Mollic Gleysols developed from sands (H)
The θ r values were in general low in the soil profile (from 0.0078 to 0.0147 cm 3 cm -3 ) (Table 2).The values of θ s at 5-15 cm were higher vs. all the other depths (p<0.05).1/α and n had a similar vertical distribution with maxima at the depth of 0-15 cm (81.55 cm and 1.369, respectively) and minimum (30.9 cm, 1.287) at the depth of 30-40 cm.

Interrelations of van Genuchten parameters, soil type, and soil texture
The data presented in Fig. 2 show that the depth-averaged means of θ r varied from 0.0266 to 0.046 cm 3 cm -3 in 3 of the 4 fine-textured soils, including Luvisols derived from silt formations and from loess (A, C) and Phaeozems from loess (D); they were significantly higher (p<0.05)than the values ranging from 0.0083 to 0.0113 cm 3 cm -3 in all the coarse-textured soils, including Luvisols derived from loams and sands (E, G) and Mollic Gleysols derived from sands (H).In the case of the fine-textured Mollic Gleysols from loess-like silt, the θ r value was not different (p<0.05) from that in each soil within the coarse-textured group (E-H).
Also, θ s in the soils were higher in the fine-textured group (0.3996 to 0.4325 cm 3 cm -3 ) than in the coarse-textured soils (0.3577-0.3785 cm 3 cm -3 ).In most cases, the θ s values of the fine-vs.coarse-textured soils were statistically significantly different (p<0.05).
The mean soil water matric potentials at which air starts entering the soil matrix (1/α) varied within the fine-textured soils from 137.9 cm in Mollic Gleysols (B) to 275.2 cm in Luvisols (C) and within the coarse-textured soils from 57.5 cm in Mollic Gleysols derived from sands (H) to 82 cm in Mollic Gleysols derived from loams (F).In most cases (except B and F Mollic Gleysols), the differences in the 1/α values between each fine-textured soil vs. each coarse-textured soil were significant (p<0.05),irrespective of the genetic soil type.
The mean values of the shape parameter (n) varied in the fine-textured soils from 1.3626 in Mollic Gleysols (B) to 1.5799 in Luvisol (C) and within the coarse-textured soils from 1.2387 in Luvisols (E) to 1.3276 Mollic Gleysols (H) (Fig. 2).The differences in n between each fine-textured soil vs. each coarse-textured soil were significant (p<0.05)except for the fine-textured B soil and all the coarse-textured soils.The higher mean values of the shape parameter (n) in the fine-textured (A-D) soils (1.3626-1.5799)than in the coarse-textured (E-H) soils (1.25-1.32)indicate greater steepness of SWRCs in the latter.
Figure 3 shows that the soil type-averaged means of θ r varied insignificantly from 0.0181 at 30-40 cm to 0.0264 at 80-90 cm.The θ s values were higher (p<0.05) at the 5-15 cm depth than at the other depths.Both 1/α and n values were higher (p<0.05) at 5-15 than at 55-65 cm.The analysis of the mean values and standard deviations indicates that the distribution of the van Genuchten parameters in soil pedon depths was in general more discontinuous in the fine-textured than coarse-textured soils.
The high coefficients of determination R 2 (0.885-1.00) (Table S1) showed that the van Genuchten soil water retention model yields acceptable results for the large set of data measured for different genetic soil types, textures, and pedon depths on a large scale.

DISCUSSION
Our results showed that the residual water content (θ r ) retained in small pores was, in general, higher (0.0266-0.046 cm 3 cm -3 ) in the fine-textured soils (A, C, D) derived from silt formations and loess (except the lower value in soil B derived from loess-like deposits) than in the coarse-textured soils (E-H) derived from sands and loams (0.0083 to 0.0113 cm 3 cm -3 ), irrespective of the genetic soil type (Fig. 2).The higher θ r values in the fine-than coarse-textured soils reflect a positive association between particle size and pore size and the related stronger adsorption capacity (e.g.Kumar et al., 2019).Noteworthy is the relatively low θ r in Mollic Gleysols (B) derived from loess-like deposits compared to Phaeozems and Luvisols and Mollic Gleysols derived from loess.This difference can be related to the greater content of the sand fraction (2-0.05mm) in soils derived from loess-like deposits (B) than from loess (C, D) (Table 1).The greater amount of the sand fraction in loesslike deposits (B) is attributed to their origin from the weathering of Holocene dust and fluvioglacial and limnoglacial sediments in contrast to loess deposited by wind (Maruszczak, 2000).Also, the saturated water content (θ s ) was greater in the fine-textured (0.3996-0.4325 cm 3 cm -3 ) vs. coarse-textured soils (0.3577-0.3785 cm 3 cm -3 ), which can be attributed to better aggregation (e.g.Bieganowski et al., 2018) and greater contribution of large inter-aggregate pores (structural porosity) (Lipiec et al., 2007).
The matric water potentials at which air starts entering the soil matrix (1/α) were significantly higher (137.9-275.2cm) in the fine-textured (A-D) than in coarse-textured (E-H) soils (from 57.5 to 82 cm).The higher values of the air entry matric potential promote infiltration and storage of water during rainfall periods and impede drainage and loss of water during prolonged drying periods, thereby increasing resistance to extreme weather conditions associated with progressive climate changes (Bondì et al., 2022).The resistance can be further enhanced by the higher field water capacity (FWC) in the fine-textured (0.327-0.377 cm 3 cm -3 ) vs. coarse-textured (0.217-0.317 cm 3 cm -3 ) soils (Table 1).Irrespective of the texture, the Mollic Gleysols (B, F, H) and Phaeozems (D) compared to the other soil types can be more resilient to increased drought incidence due to the higher average content of SOC in the whole soil pedon (6.26-9.8 vs. 2.90-3.35g kg -1 ) through increasing water storage (Lipiec et al., 2021).The lower 1/α values of the coarse-textured soils signify larger sizes of macropores (Fu et al., 2021), which result in better drainage and aeration following soil saturation with water, as they empty first as the matric potential decreases (Jabro and Stevens, 2022).Further ongoing studies aiming at the estimation of hydraulic conductivity as a function of the water matric potential based on the water retention and saturated hydraulic conductivity data collected using the van Genuchten equation will improve the evaluation of the resistance to climate change in terms of movement and accessibility of water for plant roots in various site conditions.
Overall, our study demonstrated that the differences in the values of all the vG parameters were appreciably high between the soils from the different textural groups, irrespective of the genetic soil type, and much lower and in general statistically insignificant (p<0.05) between the genetic soil types within the same textural groups.For example, within the coarse-textured soils, all the vG parameters were not different between two Luvisols (E and G) and between two Mollic Gleysols (F and H).This observation indicates the suitability of soil texture data for the prediction of vG parameters in large scales that require a description of hydraulic properties at smaller core and/or pore scales (Hopmans et al., 2002;Vogel, 2019).The suitability can be enhanced by the worldwide availability of quantitative data on textural fractions in soil geographic databases (e.g.Batjes et al., 2020;Hengl et al., 2017) or the Soil Quality Mobile App (SQAPP) (Fleskens et al., 2020).
Using the same sampling and measurement procedure with pressure plates in this study was suitable for the reliable comparison of soil water retention between different soils at the regional scale.However, recent studies revealed substantial differences in the measurement of soil water retention curves due to variability in measurement procedures used in different laboratories (Mosquera et al., 2021;Guillaume et al., 2023).The variability results mostly from the different devices used, sample size, saturation procedure, inadequate hydraulic contact in suction plate or pressure plate methods, or weighting technique (Guillaume et al., 2023).The mean inter-laboratory variability in the wet part of the SWRCs was more essential than the variability due to intrinsic differences between soil samples.Another source of variability of soil water retention outcomes from measurements at field and laboratory scales.In a study by Pachepsky et al. (2001) field vs. laboratory measurement of water retention in fine-textured soils was significantly smaller due to different soil volumes and spatial scales.To improve both comparison of differently determined SWRC and hydraulic databases further studies are required for standardization and harmonization of methods (Guillaume et al., 2023).

CONCLUSIONS
The results of this study showed the following findings: 1.The van Genuchten type function fitted very well to the measured soil water retention parameters, including residual water content, saturated water content, matric water potentials at which air starts entering the soil, and the shape parameter (R 2 > 0.885) for a range of soils with different texture and genesis in central and south-eastern Poland.This indicates good performance of the van Genuchten model at a large regional scale.
2. The van Genuchten parameters were higher in the fine-textured compared to coarse-textured soils.They were less influenced by the genetic type than the soil texture.
3. The vertical distribution of the van Genuchten parameters was in general more discontinuous in the fine-textured than coarse-textured soils.
4. The results support our hypothesis that the soil texture and genetic type have a different effect on the van Genuchten hydraulic parameters across the pedon and regional scale.

Conflicts of Interest:
The authors declare no competing interests.
Data availability: Data will be made available on request from the corresponding author -Jerzy Lipiec.

Fig. 2 .
Fig. 2. Mean comparisons of the main effect of soils on residual water content (θ r ), saturated water content (θ s ), matric water potentials at which air starts entering the soil (1/α where α is a fitting parameter related to the inverse of the air entry potential), and fitting parameter that determines the shape of the soil water retention curve (n).Horizontal lines, vertical bars, and dots indicate the median, and range of non-outliers and outliers.Different letters indicate statistically significant differences (p<0.05).

Fig. 3 .
Fig. 3. Mean comparisons of the main effect of depths on residual water content (θ r ), saturated water content (θ s ), and matric water potentials at which air starts entering the soil (1/α where α is a fitting parameter related to the inverse of the air entry potential), and fitting parameter that determines the shape of the soil water retention curve (n).Horizontal lines, vertical bars, and dots indicate the median, and range of non-outliers and outliers, respectively.Different letters indicate statistically significant differences (p<0.05).
Ta b l e 1. Means and standard deviations of sand, silt and clay contents (%), bulk density (BD), field water capacity (FWC), and saturated hydraulic conductivity (Ksat) of the studied soils A -Luvisols developed from silt formations, B -Mollic Gleysols developed from silt formations, C -Luvisols developed from loess, D -Phaeozems developed from loess, E -Luvisols developed from loams, F -Mollic Gleysols developed from loams, G -Luvisols developed from sands, H -Mollic Gleysols developed from sands.