Least Limiting Water and Matric Potential Ranges of Agricultural Soils with T Calculated Physical Restriction Thresholds Renato P

Agricultural Water Management 240 (2020) 106299

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Agricultural Water Management

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Least limiting water and matric potential ranges of agricultural soils with T calculated physical restriction thresholds Renato P. de Limaa,*, Cássio A. Tormenab, Getulio C. Figueiredoc, Anderson R. da Silvad, Mário M. Rolima a Department of Agricultural Engineering, Federal Rural University of Pernambuco, Rua Dom Manoel de Medeiros, s/n, Dois Irmãos, 52171-900, Recife, PE, Brazil b Department of Agronomy, State University of Maringá, Av. Colombo, 5790, 87020-900, Maringá, Paraná, Brazil c Department of Soil Science, Federal University of Rio Grande do Sul, Av. Bento Gonçalves, 7712, 91540-000, Porto Alegre, RS, Brazil d Agronomy Department, Goiano Federal Institute, Geraldo Silva Nascimento Road, km 2.5, 75790-000, Urutai, GO, Brazil

ARTICLE INFO ABSTRACT

Keywords: The least limiting water range (LLWR) is a modern and widely used soil physical quality indicator based on Agricultural water management predefined limits of water availability, aeration, and penetration resistance, providing a range ofsoilwater Soil physical restrictions contents in which their limitations for plant growth are minimized. However, to set up the upper and lower Water availability limits for a range of soil physical properties is a challenge for LLWR computation and hence for adequate water management. Moreover, the usual LLWR is given in terms of the soil water content in which only for field capacity and permanent wilting point, the matric potential range is known. In this paper, we present a procedure for calculating LLWR using Genuchten’s water retention curve parameters and introducing the least limiting matric potential ranges of agricultural soils, which we named LLMPR, defined as the range of matric potential for which soil aeration, water availability, and mechanical resistance would not be restrictive to plant growth. Additionally, we calculated the minimal air-filled porosity, field capacity, permanent wilting point, and limiting soil penetration resistance thresholds which define the upper and lower limits of LLWR and LLMPR. Finally, we present some application examples using experimental data (from cultivated and forest soils) and developed an algorithm for their calculation in the R software. The calculated soil physical restriction thresholds were sensitive to changes in soil structure and clay content and were changeable rather than fixed. Based on experimental data, our calculations with the calculated parameters showed that an increase in LLWR and its corresponding LLMPR could be achieved with improvements in soil structure. Higher water content at field capacity, as well as a larger soil penetration resistance threshold to a given root elongation rate were observed in the structured in comparison to the cultivated soil. The LLWR and LLMPR as presented in this study was computationally implemented as an R function (R software), named llwr_llmpr, and in an interactive web page, both available in the R package soilphysics, version 4.0 or later, available from https://arsilva87.github.io/soilphysics/ or CRAN (http://cran.r-project.org/web/packages/soilphysics/index.html).

1. Introduction impose restrictions for plant growth, even within the range of PAW (Letey, 1985; Silva et al., 1994; Groenevelt et al., 2001; Asgarzadeh Plant-available water (PAW) is a well-known concept that was first et al., 2014; Lima et al., 2016). proposed by Veihmeyer and Hendrickson (1927, 1931)(Asgarzadeh Temporal and spatial changes in water content interact with the soil et al., 2014). It is defined as the water content between field capacity structure, influencing many soil physical properties. Letey (1985) (FC) and permanent wilting point (PWP). In the absence of other considered that air-filled porosity and soil penetration resistance re- physical restrictions (e.g., soil aeration and impedance to root elonga- strictions may occur within the PAW range in such a way that water tion), plants should be able to grow within the PAW range without uptake would be limited by rising soil mechanical resistance under water stress (Letey, 1985; Silva et al., 1994). However, due to the drying or reducing root oxygen supply under wetter conditions. For this complex nature of soil particles and soil structure changes induced by approach, he introduced the term non-limiting water range (NLWR) to agricultural traffic, both aeration and mechanical impedance may characterize the water content range in which plant growth should not

⁎ Corresponding author. E-mail address: [email protected] (R.P. de Lima). https://doi.org/10.1016/j.agwat.2020.106299 Received 17 March 2020; Received in revised form 25 May 2020; Accepted 28 May 2020 0378-3774/ © 2020 Elsevier B.V. All rights reserved. R.P. de Lima, et al. Agricultural Water Management 240 (2020) 106299 be restricted by aeration, penetration resistance, and soil water poten- (from cultivated and forest soils) and developed an algorithm for cal- tial. Silva et al. (1994) quantitatively refined the NLWR concept in- culation in the R software. troduced by Letey (1985) and renamed it the least limiting water range (LLWR), which takes into account the water content range for which 2. Theoretical formulation soil aeration, soil penetration resistance, and soil water potentials at FC and PWP should impose minimal stress on plant growth. 2.1. Least limiting water (LLWR) and matric potential ranges (LLMPR) Generally, the LLWR is given in terms of soil water content (e.g., Silva et al., 1994; Leão and da Silva, 2004; Lima et al., 2016), and only To avoid any confusion in signals and for the mathematical for- the matric potentials at the FC and PWP are known, because they are mulation, the matric potential (Ψ) will be described in terms of water assigned as input physical restriction thresholds for the calculation of tension (h), which can be given as h = | Ψ |. To calculate LLWR and the LLWR (Silva et al., 1994; Leão and da Silva, 2004; Lima et al., LLMPR, both water retention and penetration resistance curves are 2016). This means that the matric potential at limiting air-filled por- necessary. Genuchten’s model (van Genuchten, 1980) (Eq. 1) is used to osity and mechanical resistance is unknown in the current LLWR ap- describe the soil water retention curve, whereas the model proposed by proach. Approaches using the matric potential ranges at which the soil Busscher (1990) (Eq. 2) is applied to describe the behavior of soil pe- physical restriction thresholds occur have been applied in the studies of netration resistance as a function of water content: Groenevelt et al. (2001) and Asgarzadeh et al. (2010) for calculation of 1 n n 1 the Integral Water Capacity (IWC) (see also Asgarzadeh et al., 2014 and =r + ( s r )[1+ (h ) ] (1) Lima et al., 2016). The calculation of the LLWR in terms of matric Q= d e f potential could allow agricultural management using both the water s (2) content and the matric potential (e.g., using tensiometers), which where θ is the soil volumetric water content (m3 m−3); h is the water would be useful for applications at the field scale (Tormena et al., tension (hPa); θs and θr are the saturated and residual water contents 3 −3 1999). (m m ), respectively; Q is the soil penetrometer resistance (MPa); s The LLWR is a widely used soil physical quality indicator for water is the soil bulk density (Mg m−3); and α and n (Eq. 1), as well as d, e, management (e.g., Safadoust et al., 2014; Ferreira et al., 2017; Oliveira and f (Eq. 2), are the fitting parameters. et al., 2019), but knowledge of the upper and lower limits (air filled- Using defined values of field capacity (hFC, hPa) and permanent porosity, FC, PWP, and soil penetration resistance) for a range of soil wilting point (hPWP, hPa), the volumetric soil water content at the field properties is a major challenge for LLWR applications at the field scale capacity (θFC) and permanent wilting point (θWP) can be calculated (Clark et al., 2003; Bengough, 2012; Czyż and Dexter, 2012; Dexter using Genuchten’s soil water retention curve model by applying Eqs. 3 et al., 2012; Assouline and Or, 2014; van Lier and Wendroth, 2016; van and 4: Lier, 2017; Meskini-Vishkaee et al., 2018; Pulido-Moncada and 1 n 1 Munkholm, 2019; Lima et al., 2020). Silva et al. (1994) suggested a FC =r + ( s r )[1+ (hFC ) ] n (3) 3 −3 minimal aeration porosity of 0.10 m m , a matric potential at field 1 n 1 capacity and permanent wilting point of -100 and -15,000 hPa, re- WP =r + ( s r )[1+ (hPWP ) ] n (4) spectively, and a limiting soil penetration resistance of 2.0 MPa as the The θ at which Q reaches a critical value (Qcritical, MPa) for plant physical restriction thresholds of the LLWR. However, recent studies growth, θQcritical, can be calculated from Eq. (2), using Eq. (5), whereas show that these thresholds depend on the plant's response, soil porosity, the h corresponding to the θQcritical (hQcritical) can be calculated using and hydraulic and mechanical properties of soil, instead of being ar- Genuchen’s model, given in terms of h as a function of θ (Eq. 6): bitrarily applied (Meskini-Vishkaee et al., 2018; Pulido-Moncada and 1 Munkholm, 2019; Wiecheteck et al., 2020). e Qcritical For example, Pulido-Moncada and Munkholm (2019) suggest that Qcritical = d f the minimum air filled-porosity could be calculated as a function of s (5) minimum relative gas diffusion for plant oxygen supply. Assouline and n/(1 n ) 1/n Or (2014) provide a simple procedure for estimating field capacity as a 1 Qcritical r hQcritical = 1 function of water retention curve components. Czyż and Dexter (2012) s r (6) suggest that the wilting of plants may occur at the hydraulic cut-off of 3 −3 soil, which Dexter et al. (2012) defined as the matric potential at which Based on a minimal air-filled porosity ( a, m m ) threshold to convective water flow ceases, even under an applied pressure gradient. ensure plant oxygen supply, the θ value which allows , a, can be h Bengough (1997) and Moraes et al. (2018) estimated the impact of calculated using Eq. 7, whereas the h corresponding to the , a, can mechanical impedance in terms of root elongation rate and penet- be calculated using Genuchen’s model by applying Eq. 8: rometer resistance. However, only a few studies (e.g., Pilatti et al., a = a (7) 2012; Meskini-Vishkaee et al., 2018; Pulido-Moncada and Munkholm, n/(1 n ) 1/n 2019) have updated the critical limits of the LLWR and compared their 1 r h = a 1 results with the usual thresholds suggested by Silva et al. (1994). a s r (8) Meskini-Vishkaee et al. (2018) and Wiecheteck et al. (2020) observed 3 −3 experimentally that different plant species respond differently tophy- where is the soil total porosity (m m ), which is equal to θs and can −3 sical soil restrictions and thresholds imposed by soil with contrasting also be expressed in terms of and particle density ( p, Mg m ) by soil textures. applying =s = [1 (s / p )]. In this paper, we present a procedure for the calculation of the LLWR using Genuchten’s water retention curve parameters. We in- 2.2. Soil physical restriction thresholds troduce the least limiting matric potential ranges of agricultural soils, which we named LLMPR and could be defined as a range of matric 2.2.1. Plant-available water (PAW): field capacity, and permanent wilting potential for which soil aeration, water availability, and mechanical point impediment would not be restrictive to plant growth. Additionally, we Instead of using the widely used θ at h of 100 hPa to represent field calculated the minimal aeration porosity, field capacity, permanent capacity (e.g., Silva et al., 1994; Leão and da Silva, 2004; Lima et al., wilting point, and limiting soil penetration resistance thresholds. 2016), we used the approach given by Meskini-Vishkaee (2018), which Finally, we present some application examples using experimental data was developed by Assouline and Or (2014), for calculation of hFC, based

2 R.P. de Lima, et al. Agricultural Water Management 240 (2020) 106299 on Genuchten’s parameters n and α, as given in Eq. (9): elongation rate), it would be possible to apply Eq. 16 and estimate the Q 1n 1 (1 2n )/ n critical for a given RET, so that Eq. 16 could be written as follows (Eq. hFC = 17): n (9) ln(RET ) Qcritical = To represent the hPWP, we assumed that the wilting of plants may x (17) occur at the hydraulic cut-off of soil (hco), which Dexter et al. (2012) defined as the h at which convective water flow ceases, even under an applied pressure gradient. For the situation at which h > hco (i.e., 3. Material and methods dryer soil condition), only the residual and immobile water remains. Dexter et al. (2012) and Czyż and Dexter (2012) proposed empirical 3.1. Experimental data relationships to estimate hco as a function of clay content (%). Thus, we assumed hPWP as equal to hco for delimiting the lower limit of PAW: In this paper, applications for calculation of the LLWR and LLMPR (3.514+ 0.0250Clay) were made using experimental data. Undisturbed soil cores were sam- hPWP= h co = 10 (10) pled at an Experimental Farm of the State University of Maringá (see Araújo et al., 2004), located in Maringá (23°21’S, 52°03'W), Paraná 2.2.2. Soil aeration restrictions state, southern Brazil. The soil was classified as Oxisol (Soil Survey The relative gas diffusivity (Ds/D0) in the soil can be estimated as a Staff, 2014), with sand, silt, and clay contents of 760, 10, and 230 g function of and a, using the classical model proposed by Millington kg−1, respectively. and Quirk (1961). Thus, the to supply a minimal Ds/D0 value of 0.005 Sampling was performed in two sites with distinct land uses: native (Grable and Siemer, 1968; Schjønning et al., 2003; Berisso et al., 2012; forest and cultivated soil. The native forest site consisted of an intact Pulido-Moncada and Munkholm, 2019) can be calculated using Eq. native forest fragment (semi/decidual seasonal forest) adjacent to the (12): cultivated site, whereas the cultivated area consisted of a con- D ventionally tilled field (disk plow and harrowing), cultivated during 20 s = a 2 consecutive years with different crops (maize, oats, sorghum, soybean, D0 (11) and cassava). At the sampling time, the soil was cultivated with cas- 2 (1/ ) a= [(/)]DD s 0 (12) sava. Undisturbed soil cores were randomly taken at a depth of 0–0.20 m where β is an empirical parameter, here assumed as 10/3, which was within each experimental site, using steel rings of 0.05 m diameter and first suggested by Millington and Quirk (1961). Later, van Lier (2001) 0.05 m height, totaling 24 samples per experimental site. The soil cores verified that the value 10/3 for β resulted in the best agreement be- were saturated by capillary rise and equilibrated to one of the following tween calculated and typical values reported in the literature. water tensions (h): 10, 20, 40, 60, 80, and 100 hPa, using a tension table and 250, 500, 1,000, 2,000, 4,000, 8,000, and 15,000 hPa via a pres- 2.2.3. Soil mechanical resistance for root growth sure plate apparatus. At hydraulic equilibrium, the soil cores were Bengough (1997) and Moraes et al. (2018) suggest that better ap- weighed for each h for the determination of the water content. For proximations of root growth can be given in terms of root elongation fitting of the soil water retention curve and to demonstrate thecalcu- rate (RET). Bengough (1997) and Moraes et al. (2018) show that RET lation procedures, we used samples for maximum, minimum, and mean Q can be estimated as a function of using an exponential equation (Eq. values of soil bulk density for each experimental site. Q 15), whereas the at which a given RET occurs, RET , can be estimated Another set of 24 soil cores per site was sampled to determine the using Eq. 16: soil penetration resistance curve. Soil penetrometer resistance (Q) was RET= exp( xQ ) (15) measured with an electronic laboratory penetrometer at a penetration rate of 10 mm min–1, using a 60° cone angle and a diameter of 4 mm. ln(RET ) QRET = Finally, the cores were oven-dried at 105 °C for 24 h to determine bulk x (16) density and soil water content. The parameters of this measurement are where x is an empirical parameter and RET is given in a scale from 0 to also available in Araújo et al. (2004). 1 (i.e., from 0 to 100 %). Moraes et al. (2018) explain that biopores may facilitate root elongation and change the relationship between RET and 3.2. Least limiting water (LLWR) and matric potential ranges (LLMPR) soil strength. Thus, Moraes et al. (2018) suggest values of x = -0.4325 calculations and x = -0.3000 for soil without and with biopores, respectively, which could be analogously compared to soil without and with a structure or Based on the experimental data described previously, we fitted van with and without tillage practices. Genuchten’s water retention curve (Eq. 1) for the three soil bulk density By applying Eq. 16, it is possible to estimate, for example, the at levels (classes separated within each site) obtained within the native which RET is halved by using RET = 0.5. Assuming QQRET= critical (see forest and cultivated sites (Table 1), which we named minimum, mean, Eq. 5) (representing the critical penetrometer resistance for a given root and maximum soil bulk density levels. Additionally, Busscher’s

Table 1 Water retention curve fitted parameters (Genuchten’s model) for minimum, medium, and maximum bulk density levels of native forest and cultivatedsoils.

−3 3 −3 3 −3 −1 Land use Soil bulk density levels Soil bulk density (Mg m ) θr (m m ) θs (m m ) α (hPa ) n

Minimum 1.26 0.1347 *** 0.5271 *** 0.0303 *** 2.1165 *** Native forest Mean 1.39 0.1337 *** 0.4784 *** 0.0211 *** 2.3694 *** Maximum 1.52 0.1246 *** 0.4095 *** 0.0228 *** 1.8336 *** Minimum 1.68 0.1087 *** 0.3669 *** 0.0221 ** 1.5785 *** Cultivated Mean 1.76 0.1186 *** 0.3240 *** 0.0136 ** 1.5290 *** Maximum 1.84 0.1161 *** 0.2935 *** 0.0290 * 1.4362 ***

‘****’ ‘***’ ‘**’ θs: volumetric water content at saturation; θr: residual volumetric water content; α: scaling parameter; n: shape parameter. p < 0.001; p < 0.01; p < 0.05; ‘*’ p < 0.1.

3 R.P. de Lima, et al. Agricultural Water Management 240 (2020) 106299

Table 2 Physical restriction thresholds used for calculation of the least limiting water and matric potential ranges by the usual (Silva et al., 1994) and calculated (Section 2.2) thresholds.

3 −3 Land use Thresholds Soil bulk density levels a(m m ) hFC (hPa) hPWP (hPa) Qcritical (MPa)

Minimum 0.10 100 15,000 2.0 Usual Mean 0.10 100 15,000 2.0 Maximum 0.10 100 15,000 2.0 Forest Minimum 0.1389 87 12,274 2.3 Calculated Mean 0.1310 112 12,274 2.3 Maximum 0.1194 138 12,274 2.3 Minimum 0.10 100 15,000 2.0 Usual Mean 0.10 100 15,000 2.0 Maximum 0.10 100 15,000 2.0 Cultivated Minimum 0.1117 178 12,274 1.6 Calculated Mean 0.1037 306 12,274 1.6 Maximum 0.0977 163 12,274 1.6

a: air-filled porosity; hFC: water tension at field capacity; hPWP: water tension at the permanent wilting point; Qcritical: critical penetration resistance for 50 % of the root elongation rate.

penetrometer resistance model was fitted for the range of bulk density (2019) suggest a power model for the estimation of Ds/D0 as a function and soil water contents corresponding to the applied h to obtain the of , for which an empirical parameter is necessary. Here, we propose parameters d, e, and f, which were estimated as 0.0132, -1.3406, and the use of the classical model from Millington and Quirk (1961) (Eq. 5.3229 (p < 0.05; R2 = 0.84), respectively, for the native forest soil 11) for the calculation of , which Neira et al. (2015) described as a and 0.0028, -2.0592 and 5.3229 (p < 0.05; R2 = 0.84), respectively, mechanistic model. Moldrup et al. (2004) verified that among the fre- for the cultivated soil (Araújo et al., 2004). quently used soil-type-independent models for estimation of Ds/D0, the To calculate the LLWR and LLMPR, we applied the procedure de- Millington and Quirk (1961) model performed best. The Millington and scribed in Section 2, using the usual (i.e., Silva et al., 1994) and cal- Quirk (1961) model requires only a few parameters for estimation of culated physical restriction thresholds, i.e., a , hFC, hPWP, and Qcritical, and seems to be able to provide good agreement with experimental data which resulted in the “usual” and “calculated” scenarios. A summary of (Moldrup et al., 2004). the thresholds for each scenario is given in Table 2. Specifically for Soil water tension at the field capacity (hFC), calculated by Eq. (9) calculation of Qcritical, we fixed the bulk densities given in Table 1 for (Assouline and Or, 2014), was predominantly higher than 100 hPa for each one of the classes and applied Eq. 5 using a estimated for 50 both native forest and cultivated soil, but higher values were observed

% of RET (i.e., RET = 0.5), which was calculated using Eq. 17 by ap- for the cultivated soil (Table 2). Based on the hFC, calculated using Eq. 9 plying x = -0.3000 and x = -0.4325 for native forest (with biopores) (Table 2), in the cultivated soil, the water would still be freely draining and cultivated soils (without biopores) (Moraes et al., 2018), respec- at around 100 hPa, and therefore, hFC would be underestimated. Eq. 9 tively. shows that hFC, which is dependent on Genuchten´s parameters α and n, and the matric potential at field capacity will be somewhat larger with decreasing values of n. Table 1 shows that lower n values were obtained 4. Results and discussion for the cultivated soil, and therefore, higher hFC values were estimated for this soil (Table 2), which are greater than the usual 100 hPa (Silva 4.1. Physical restriction thresholds et al., 1994). The formulation given by Assouline and Or (2014) is described as a The calculated a (Eq. 12) was slightly larger than the usual self-consistent criterion based on soil internal drainage dynamics, suggested by Silva et al. (1994) for native forest soil, whereas for cul- which describe the calculated hFC (Eq. 9) as a marked loss of hydraulic tivated soil, was rather similar to the generally suggested continuity which characterizes the field capacity. After numerical si- 0.10 m3 m−3 (Silva et al., 1994)(Table 2). Based on Eq. 12, for a mulations and comparison with experimental data, Assouline and Or fixed value of D /D = 0.005 (as the used here) becomes dependent on s 0 (2014) argue that their results reveal remarkable consistency and pre- , which is similar to the θ given in Table 1. Thus, considering the θ of s s dictability across a wide range of soil types. the native forest and cultivated soils, it is possible to observe that is In addition to Assouline and Or (2014), recent studies from greater with an increasing θ (Tables 1 and 2). Therefore, considering a s Twarakavi et al. (2009); van Lier (2017), and Meskini-Vishkaee et al. minimal D /D for plant oxygen supply, would not be a fixed value s 0 (2018) have questioned the use of field capacity as a single value of soil (e.g., 0.10 m3 m−3), but dependent on soil total porosity. Our simula- h. Among several possible formulations for the estimation of hFC de- tion shows that for the native forest soil, an of 0.10 m3 m−3 would scribed in previous studies (e.g., Twarakavi et al., 2009; Reynolds et al., not be sufficient to provide minimal gas diffusion (D /D = 0.005). s 0 2018), an advantage of the model proposed by Assouline and Or (2014) Although we used the value of 0.005 for Ds/D0, the Millington and is that hFC is derived from the soil water retention curve and is easily Quirk (1961) model allows the use of a range of D /D as suggested by s 0 parameterized using Genuchten’s parameters, which can be extracted Grable and Siemer (1968) (i.e., D /D from 0.005 to 0.02), making it an s 0 from the same formulation of the LLWR and LLMPR proposed here. open-input model from a practical point of view. By increasing the Our calculations for hPWP, considering the hco proposed by Dexter value of Ds/D0 towards 0.02 while remains unchanged, the Millington et al. (2012), reveal that hPWP was lower than the usual threshold of and Quirk (1961) model estimates that a greater value is required to 15,000 hPa used by Silva et al. (1994) (Table 2). The hco was calculated allow the corresponding D /D . However, this model does not in- −1 s 0 as 12,274 hPa, indicating that for this clay content (i.e., 230 g kg ), corporate dynamic aspects regarding the level of organization of the following the empirical equation proposed by Dexter et al. (2012), porous system, which may be developed in future studies. plants should wither in wetter conditions than 15,000 hPa because after The value of Ds/D0 = 0.005 has also been suggested as a minimal the soil has reached the hco, convective water flow should cease, even plant oxygen supply by Schjønning et al. (2003), Kadžienė et al. (2011), under an applied pressure gradient by the plants. Dexter (2004) and Berisso et al. (2012), and Pulido-Moncada and Munkholm (2019). Dexter et al. (2012) explain that the clay content governs textural However, Kadžienė et al. (2011) and Pulido-Moncada and Munkholm

4 R.P. de Lima, et al. Agricultural Water Management 240 (2020) 106299 porosity, and therefore, particles smaller than 2 μm (i.e., clay) are should be maintained for conventional tillage. However, it should be especially important because most of the specific surface area (and increased to 3.0–3.5 MPa under no-tillage and/or minimum tillage be- therefore adsorption) occurs on these smallest particles. This somehow cause of the predominance of biopores (presenting a soil environment justifies the positive correlation of hco and clay content found by Dexter more similar to forest, i.e., with more biopores). In a recent study, Lima et al. (2012). Overall, the model from Dexter et al. (2012) demonstrated et al. (2020) found a severe contrast for soil penetration resistance that plants should wither in sandy soil under a high soil water potential, behavior affected by tillage systems, which seems to have been influ- rather than in clay soils. enced by soil structure. Investigating the hydraulic cut-off and plant wilting relationship, Several studies applying the LLWR concept have used 2.0 MPa as Czyż and Dexter (2012) demonstrated that the h at the permanent Qcritical (e.g., Leão and da Silva, 2004; Lima et al., 2016; Tormena et al., wilting point does not appear to be a single value, as first proposed by 2017; Pulido-Moncada and Munkholm, 2019), but these studies make Briggs and Shantz (1912) and Veihmeyer and Hendrickson (1928). Czyż no reference to an expected loss in the growth rate of any root para- and Dexter (2012) tried to show, for a range of soil textural classes, that meter. Approaches for estimating the soil penetrometer resistance, re- drainage often ceases at h < 15,000 hPa due to the phenomenon of quired to reduce the rate of root elongation by half, were proposed by hydraulic cut-off. Furthermore, they highlight that it is interesting to Dexter (1987) and discussed by Silva et al. (1994). However, the cal- note that this explanation is published 100 years after Briggs and culation of LLWR proposed by Silva et al. (1994) was based on the Shantz (1912). In an experiment comparing the classical permanent assumption that the limiting value of soil resistance is constant at wilting point concept of soil to the biological wilting of wheat and 2.0 MPa, which has been a usual threshold used for many studies using barley plants under contrasting soil textures, Wiecheteck et al. (2020) the LLWR. Furthermore, the fixed threshold does not consider the effect observed that wheat and barley plants withered under wetter condi- of soil structure on the reduction/increase in Qcritical, for which the tions than the h of 15,000 hPa for soil with lower clay content, corro- studies of Bengough (1997) and Moraes et al. (2018) showed to be borating the empirical equation suggested by Dexter et al. (2012) (Eq. relevant. 10). There are not many functions for the estimation of root elongation It is important to highlight that we used the empirical equation (Eq. rate as a function of soil penetrometer resistance. However, the studies 10) proposed by Dexter et al. (2012) to illustrate the understanding of of Dexter (1987); Bengough (1997), and Moraes et al. (2018) seem to the application of the hydraulic cut-off as the lower limit of LLWR and show that there is a need to know not only the critical limit of penet- LLMPR. However, Dexter et al. (2012) detail two procedures that are rometer resistance for root growth impediment, but also the rate of loss based on the water retention curve parameters proposed by Groenevelt associated with the increase of this penetrometer resistance. Note that, and Grant (2004) and Dexter et al. (2008). Thus, it is possible to cal- within the LLWR approach, water content could be managed to achieve culate the hco from experimental data by fitting the parameters of a Qcritical that would only reduce a relative growth rate. Groenevelt and Grant (2004) and Dexter et al. (2008) to the water retention curves and to apply the procedures described by Dexter et al. 4.2. Least limiting water (LLWR) and matric potential ranges (LLMPR)

(2012). In this study, we chose to apply the estimated hco (as a function of clay content) because of the complexity of introducing two more Except for the native forest soil at the minimum soil bulk density, water retention curves on the calculation procedure. the LLWR was reduced from usual to the calculated physical restriction The assumption that the permanent wilting point is not a single threshold scenarios (Fig. 1). Fig. 1 shows that for the land uses ex- value of h has been experimentally confirmed in several studies. The amined in this study (native forest and cultivated soil), there was an permanent wilting point reached values of h from 15,000 hPa for cotton overestimation of the LLWR calculated with the usual thresholds in and sorghum (Savage et al., 1996), 22,000–30,000 hPa for maize (Hsieh relation to that calculated. However, as the calculated thresholds are et al., 1972), and 37,000 hPa for pepper (Rawlins et al., 1968). The dynamic and dependent on soil porosity (or soil structure) and water solution proposed by Dexter et al. (2012) provides a prediction tool retention characteristics (see discussion in Section 4.1), this over- related to soil particle size (with a significant relationship with clay), estimation scenario should not always be predominant. but it seems that plant mechanisms would have to be added to pre- The graphic solution model for LLWR and LLMPR, using the cal- dictions in future studies (van Lier et al., 2006; Czyż and Dexter, 2012; culation procedure presented in Section 2.1., is given in Fig. 2. To il- Hosseini et al., 2016; Wiecheteck et al., 2020). For example, the study lustrate the graphic solution only, Fig. 2 shows the graphic solutions for carried out by Wiecheteck et al. (2020) indicates that wheat plants were LLWR and LLMPW only for the minimum bulk density (Table 1) of the more drought-tolerant than barley plants. cultivated soil, considering both usual and calculated physical restric-

The calculated Qcritical for 50 % of RET was calculated as 2.3 and tion threshold scenarios. All other physical restriction limits in terms of 1.6 MPa for native forest and cultivated soils, respectively. The higher θ and h, which delimited LLWR and LLMPR, are presented in Tables 3

Qcritical values for the native forest soil consider that roots encounter a and 4. network of cracks and biopores such that the roots of plants are able to Fig. 2 shows that the LLWR and LLMPR for the minimum soil bulk have higher elongation rates for a larger Q range (Bengough, 1997; density of the cultivated soil were delimited by field capacity and soil Moraes et al., 2018), whereas for cultivated soil without biopores, 50 % penetration resistance, regardless of the applied usual or calculated of the RET would be reached at lower Q values than the usual threshold thresholds. However, LLWR and LLMPR were greater when the physical of 2.0 MPa. This means that the degraded soil structure in cultivated restriction thresholds were applied as usual in contrast to using the soil causes greater restrictions for root elongation, and this is reflected calculated procedure. Table 3 shows that the LLWR was reduced from in the lower critical soil penetration resistance value (Bengough et al., 0.1003 to 0.0458 m3 m−3 from usual to calculated physical restriction 2011; Moraes et al., 2018). Our results highlight that the use of a thresholds, whereas the LLMPR was reduced from 708 to 287 hPa common critical penetration resistance value to calculate the LLWR for (Table 4), demonstrating a large difference between calculated LLWR studying the impact of soil management systems on soil physical quality and LLMPR using the two ascribed thresholds. may lead to inconsistent conclusions. It is well known that soil structure Fig. 3 shows how the four restrictions thresholds change as a and pore shape, size, continuity, and connectivity are altered by soil, function of bulk density for each land use and threshold scenarios (i.e., land use, and management systems (Moraes et al., 2014; Lima et al., usual and calculated). The changes in the four thresholds in the native 2020), modifying the root elongation rate. forest soil from the usual to the calculated scenarios seem to be Moraes et al. (2014) investigated critical limits of soil penetration minimal, whereas for the cultivated soil, they were considerable, de- resistance affecting plant performance in different tillage systems. They monstrating that the calculation of the thresholds was sensitive to soil suggest that the critical soil penetration resistance limit of 2.0 MPa structure and soil cultivation.

5 R.P. de Lima, et al. Agricultural Water Management 240 (2020) 106299

Fig. 1. Changes in the least limiting water range (LLWR) calculated using the usual (Silva et al., 1994) and calculated (Section 2.2) thresholds (Table 2) for the minimum, medium, and maximum bulk densities (Table 1).

Fig. 2. Illustration of the graphical solution for the least limiting water range (LLWR) and the least limiting matric potential range (LLMPR), calculated using the usual (Silva et al., 1994) (upper graphs) and calculated (Section 2.2) (lower graphs) thresholds for the minimum bulk density (Table 1) of the cultivated soil. AFP: air- filled porosity; FC: field capacity; PWP; permanent wilting point; Q: soil penetration resistance.

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Table 3 Water contents at air-filled porosity ( a), field capacity ( FC), permanent wilting point ( PWP), and limiting soil penetration resistance ( Qcritical), calculated using the usual (Silva et al., 1994) and calculated (Section 2.2) thresholds (Table 2). LLWR: Least limiting water range.

Land use Thresholds Soil bulk density levels a FC PWP Qcritical LLWR (m3 m−3)

Minimum 0.4271 0.2432 0.1351 0.0573 0.1080 Usual Mean 0.3784 0.2469 0.1338 0.0849 0.1131 Maximum 0.3095 0.2555 0.1268 0.1381 0.1174 Forest Minimum 0.3882 0.2585 0.1352 0.0515 0.1233 Calculated Mean 0.3473 0.2320 0.1339 0.0762 0.0981 Maximum 0.2901 0.2285 0.1272 0.1240 0.1013 Minimum 0.2669 0.2575 0.1177 0.1572 0.1003 Usual Mean 0.2240 0.2662 0.1309 0.1852 0.0388 Maximum 0.1935 0.2211 0.1286 0.2074 0 Cultivated Minimum 0.2551 0.2209 0.1188 0.1751 0.0458 Calculated Mean 0.2202 0.2116 0.1323 0.2063 0.0053 Maximum 0.1957 0.2034 0.1298 0.2309 0

Table 4 web page, both available in the R package soilphysics (available from Water tensions at air-filled porosityh ( a), field capacityh ( FC), permanent https://arsilva87.github.io/soilphysics/ or http://cran.r-project.org/ wilting point (hPWP), and limiting soil penetration resistance (hQcritical), calcu- web/packages/soilphysics/index.html). Basically, the function lated using the usual (Silva et al., 1994) and calculated (section 2.2) thresholds llwr_llmpr requires Genuchten’s water retention curve parameters (Table 2). LLMPR:. least limiting matric potential range. (Table 1), Busscher's soil penetration curve parameters (d, e and f), and

Land use Thresholds Soil bulk h a hFC hPWP hQcritical LLMPR the soil physical restriction thresholds (Table 2). Although here, we density levels calculated the soil physical restriction thresholds, the user is free to (hPa) assign the thresholds in the function llwr_llmpr. The output of the function llwr_llmpr is the graphic solution for LLWR or LLMPR, as well Minimum 28 100 15,000 > 14,900 as a correspond table with the limits (in terms of θ and h) and the values Usual Mean 43 100 15,000 > 14,900 Maximum 56 100 15,000 1693 1593 of LLWR and LLMPR. Forest Minimum 37 87 12,274 > 12,186 Calculated Mean 53 112 12,274 > 12,161 Maximum 69 138 12,274 > 12,136 5. Summary and conclusions Minimum 87 100 15,000 808 708 Usual Mean 234 100 15,000 602 368 We present a new procedure for the calculation of the least limiting Maximum 220 100 15,000 145 0 Cultivated Minimum 103 178 12,274 466 287 water range (LLWR), and additionally present the least limiting water Calculated Mean 253 306 12,274 347 40 matric potential range (LLMPR). Both LLWR and LLMPR are easily Maximum 205 163 12,274 77 0 parameterized using the common Genuchten’s water retention curve, beyond the usual Busscher’s penetration resistance curve. The introduction of the LLMPR calculation allowed to determine, besides the Table 2 shows that the reduction in LLWR and LLMPR from the soil water content, the soil water potential boundaries associated with usual to the calculated scenarios of the cultivated soil was caused by an physical restrictions for plant growth. increase in hFC from 100 to 178 hPa and a decrease in Qcritical from Furthermore, we present a calculation procedure of the soil physical 2.0–1.6 MPa, which resulted in a decrease and increase in θFC and restriction thresholds that are used to calculate LLWR and LLMPR and θQcritical, respectively (Fig. 3). Based on our scenarios, these results suggest a procedure for the calculation of minimal aeration porosity, show that an increase in LLWR and its corresponding LLMPR could be field capacity, permanent wilting point, and limiting soil penetration achieved with improvements in soil structure, which results in lower h resistance thresholds. The calculated soil physical restriction thresholds at field capacity, as well as an increase in soil penetration resistance for are sensitive to changes in soil structure and clay content and are a given elongation rate. therefore changeable rather than fixed. They were able to considerably Overall, water content or water potential at the field scale should be reduce LLWR and LLMPR in native forest and cultivated soils in com- managed within LLWR and LLMPR to avoid physical restriction for parison with calculations made with the usual thresholds. Finally, based plant water uptake. Note that, besides the water content range given by on experimental data, our calculations with the calculated thresholds LLWR (first introduced by Silva et al., 1994), the corresponding LLMPR showed that an increase in LLWR and its corresponding LLMPR could presented in this study would also allow monitoring of the moisture be achieved with improvements in soil structure. The improvements in range in terms of water potential, which could be managed with ten- the soil structure could result in higher water content at field capacity siometers up to 700–800 hPa and could be useful for agricultural water as well as an increase in the soil penetration resistance threshold at a management. given root elongation rate.

4.3. Computational implementation Declaration of Competing Interest

The procedure described in the Section 2.1., which calculates LLWR The authors declare that they have no known competing financial and LLMPR, was computationally implemented as an R function (R interests or personal relationships that could have appeared to influ- software; R Core Team, 2020), named llwr_llmpr, and on an interactive ence the work reported in this paper.

7 R.P. de Lima, et al. Agricultural Water Management 240 (2020) 106299

Fig. 3. Changes in the volumetric water content (θ) at air- filled porosity (AFP) (black), field capacity (FC) (blue), permanent wilting point (PWP) (red), and soil penetration resistance (Q) (gray) of the native forest and cultivated soils as a function of soil bulk density, using the usual and calculated physical restriction thresholds. The shaded area represents the least limiting water range, of which the calculated values are given in Table 3 (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article).

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