# Hydraulic Properties of a Cultivated Soil in Temperate Continental Climate Determined by Mini Disk Infiltrometer

^{*}

## Abstract

**:**

## 1. Introduction

- (i)
- Does the MDI provide K(h) and Ks information comparable with HI?
- (ii)
- Does the MDI reflect the differences in topsoil properties caused by contrasting soil tillage operations (conventional tillage CT, reduced tillage RT, and no-tillage NT)?
- (iii)
- Is the MDI able to characterize and quantify the macropore contribution to the total water flux?
- (iv)
- How the data analysis method affects the resulting K(h) and Ks values with respect to different sources of van Genuchten [36] hydraulic parameters?

## 2. Materials and Methods

#### 2.1. Study Area Description

^{3}undisturbed soil samples per each tillage treatment and each experimental phase), organic matter content (total organic carbon content by Walkley–Black procedure [40]) were determined during each experimental phase. Collection of undisturbed soil samples was carried out within the same week as the MDI measurements were performed. Volumetric water contents prior and after the infiltration experiments by employing ThetaProbe ML2x (Delta-T Devices Ltd., UK) were also determined. Own soil specific calibration was carried out in order to obtain high measurement accuracy; determined as ± 1.5 % by vol. The following parameters in the readout unit (HH2 Moisture meter) to display the volumetric water content were set: a

_{0}= 1.859 and a

_{1}= 10.123. The four experimental phases were as follows: (1) June and July 2008 (before harvesting the preceding crop—winter wheat); (2) September 2008 (two weeks after planting the main crop—oil seed rape); (3) April 2009 (the flowering season of the main crop); and (4) June and July 2009 (before harvesting the main crop). The MDI measurements for each experimental phase were performed within one week (5, 7, 6, and 4 days for exp. phase I, II, III, and IV). The HI measurements were lasting longer, only one measurement per day could be managed (almost 1 h of measurement for each applied pressure head, ended by a soil bubbling point). The meteorological data; average and maximum daily temperatures (°C) at 2 m and daily precipitation amounts (mm) is displayed in Figure 1. More detailed evaluation of basic soil characteristics of the top 30 cm together with microbiological analysis and crop yields for the experimental site can be found in a study presented by Mühlbachová et al. [41].

#### 2.2. Devices a Data Analyses Used for Hydraulic Conductivity Determination

#### 2.2.1. Mini Disk Infiltrometer (METER Group, Inc. USA)

^{3}), which is closed at the bottom with the porous sintered stainless steel disk (0.3 cm thick with diameter of 4.5 cm); and the upper one serves for setting of the pressure head under which the infiltration takes place (from −7 to −0.5 cm). More detailed description of the devices can be found in the User´s manuals [43,44].

_{1}(L T

^{−1}) and C

_{2}(L T

^{−1/2}) are parameters related to hydraulic conductivity and soil sorptivity respectively, I (L) is the cumulative infiltration, and t (T) the time.

_{1}is the slope of the curve of the cumulative infiltration vs. the square root of time, and A is a value relating the van Genuchten parameters for 12 soil texture classes to the radius of the disk and applied pressure head. The A parameter for the silty clay loam (α = 0.01 and n = 1.23) can be calculated according to the following formula (Equation (3)) or can be taken directly from a table presented in the User´s manual. Corrected and slightly different values were presented in an updated version of the User´s manual in 2014. However, it should be stated that those values of parameter A are derived from the USDA database covering soils from United States [47].

_{E}is effective water content (dimensionless), θ

_{E}= (θ − θ

_{r})/(θ

_{r}− θ

_{s}), θ

_{s}(L

^{3}L

^{−3}) is the volumetric water content at saturation, θ

_{r}(L

^{3}L

^{−3}) is the residual volumetric water content, α (L

^{−1}) is the dimensionless parameter and m and n are fitting parameters (m = 1−1/n), K

_{r}(h) is the hydraulic conductivity at a certain applied pressure head h (L).

_{j}is the number of measurements in a particular set, Q

_{j}*(t

_{i}) are the specific measurements at time t

_{i}for the jth measurement set, β is the vector of optimized parameters, Q

_{j}(t

_{i}, β) are the corresponding model predictions for the parameter vector β, v

_{j}and w

_{ij}are weights associated with a particular measurement set or point, respectively. The weighting coefficients v

_{j}, are given by Clausnitzer and Hopmans [52], Clausnitzer et al. [53], and Šimůnek et al. [19] as v

_{j}= 1/N

_{j}σ

_{j}

^{2}. This defines the objective function as an average weighted squared deviation normalized by measurement variances. If variance of the measurement is not known, v

_{j}and w

_{ij}values are set equal to unity [17]. For all inverse solutions carried out in this study, all v

_{j}and w

_{ij}values were set to be equal to 1.

_{s}from Equation (6): (i) θ

_{s}, the saturated soil water content (individually set according to the measured data); (ii) θ

_{r}, the residual soil water content (in order to avoid fitting to the non-realistic values too close or equal to 0, the parameter was set to the value of 0.08 cm

^{3}cm

^{−3}for all soil treatments and experimental phases); (iii) l, the pore connectivity parameter was also set uniformly to the value of 0.5; (iv) additionally, the values of θ

_{final}(individually set according to the measured data) were also used as input parameters in order to improve the optimization procedure. The boundary conditions were as follows: (i) “Variable head” on the part of the soil surface, where the MDI was located; (ii) “No flux” on the rest of the soil surface and also on the sides of the domain; (iii) “Free drainage” at the bottom of the domain.

#### 2.2.2. Hood Infiltrometer (Umwelt-Geräte-Technik, GmbH., Germany)

^{−1}) is steady–state infiltration rate, K(h) (L T

^{−1}) is the unsaturated hydraulic conductivity at the applied pressure head (K(h) = K

_{s}exp (αh)), α

_{g}(L

^{−1}) is the sorptive number (Gardner’s scaling parameter), r

_{d}(L) is radius of the disc.

_{i}) and K(h

_{i+}

_{1}) at the applied pressure heads h are then calculated as follows (Equations (10) and (11)):

#### 2.3. Evaluation of Soil Water Conductive Pore System

_{i}by 73%. [56]

_{h}was calculated based on Equation (12), while contribution of each soil pores group (macro- and mesopores) to the total saturated water flux ϕ

_{i}in % was determined based on Equation (13).

^{−1}T

^{−1}) is the dynamic viscosity of water, K(h) in L T

^{−1}is the hydraulic conductivity at the particular pressure head h (L), ρ (M L

^{−3}) is the density of water, g (L T

^{−2}) is the acceleration due to gravity, π is the dimensionless Ludolph’s number and λ

_{h}(L) is the representative mean pore radius.

_{i}(%), can be calculated according to Watson and Luxmoore [57]:

_{i}) and K(h

_{i−1}) are the hydraulic conductivities (L T

^{−1}) obtained for two water pressure heads, and K

_{s}(L T

^{−1}) is the saturated hydraulic conductivity.

#### 2.4. Statistical Evaluation

## 3. Results and Discussion

#### 3.1. Basic Soil Characteristics

_{ox}) determined for each soil treatment and experimental phase are presented in Table 2. Values of particle density were within the same range during all four experimental phases on all three soil treatments, while the other characteristics were not. A significant loosening effect of soil tillage operations were found in September 2008 for RT and CT plots resulting in lower dry bulk density values and higher values of total porosity. When evaluating the organic matter content, significant differences were found between the treatments; the highest contents were determined for NT plot. The results are in agreement with findings of Çelik et al. [26], who investigated possible differences in physical properties of soils under different tillage treatments for 10 years.

_{initial}) and final (θ

_{final}) soil moisture conditions have been observed during all infiltration experiments. As reported by Matula et al. [58] and Radinja et al. [59], the MDI has shown a high susceptibility to the θ

_{initial}for the first applied pressure head. For higher θ

_{initial}, significantly smaller K(h) value was recorded, which was in accordance with findings of Zhou et al. [60]. θ

_{initial}and θ

_{final}are also essential input data for the HYDRUS 2D/3D software in order to obtain unique solution of the inverse problem. The average θ

_{initial}and θ

_{final}values are summarized in Table 3 together with the resulting values of the van Genuchten [36] parameters from Equations (5) and (6) obtained by the inverse solution of the MDI data.

^{2}coefficient, and by graphical comparison of the measured and fitted data; both were showing very good agreement between the measured and fitted data for all infiltration experiments and all applied pressure heads.

#### 3.2. Unsaturated Hydraulic Conductivity K(h)

#### 3.3. Saturated Hydraulic Conductivity Ks

^{2}between the measured and fitted infiltration data. Requirements for inverse modelling of soil hydraulic properties has been discussed by Hopmans and Simunek [67] and Kumar et al. [3] who pointed out the amount of measured variables, boundary condition setting, errors in the measured variable and type of the soil as factors affecting the inverse solution. Also Zou et al. [68] attributed the ill-posedness of the inverse problem to the high nonlinearity of the data in unsaturated flow problems. Kumar et al. [3] reported the Ks values obtained in the laboratory one order of magnitude higher than those obtained in the field and also highlighted importance of results from the laboratory as input data for the inverse modelling of the field data. More detailed study regarding the HYDRUS 2D data analysis settings would be required. Only one hydraulic model; van Genuchten [36] – Mualem [51] was used in this study. Further options are offered in the HYDRUS 2D software; e.g., Kosugi [69] log-normal model, or Durner [70] dual porosity model. The dual porosity model especially could be beneficial, because as shown further, the contribution of macropores to the total saturated flux is very significant. Significant effect of data analysis selection on resulting K(h) and Ks results are also reported by Fatehnia et al. [71].

^{2}area in order to obtain an accuracy level as suggested by Ahmed et al. [74]. Rienzner and Gandolfi [75] compared Ks values obtained by Guelph permeameter and by tension infiltrometer concluding that the Ks values obtained by tension infiltrometer are systematically lower, which is in agreement with our study where the Ks values obtained by MDI were compared to HI. However, much smaller variability in both, space and time for the tension infiltrometers has been observed when compared to our study. Reynolds et al. [76] compared the Ks values obtained by tension infiltrometer, pressure infiltrometer and soil core determination in the laboratory with the following results: (i) different methods yielded different Ks values; (ii) tension infiltrometer provided comparable results to other methods only for Ks values smaller than 10

^{−4}m s

^{−1}; (iii) the tension infiltrometer yielded the smallest CV for the cracking clay loam; (iv) the soil core laboratory method performed well on structure less sand and structured loam soil, however in the cracking clay it yielded high CV values; and (v) the pressure infiltrometer provided comparable results to the other methods. Only for the cracking clay loam soil it yielded in a large range of the Ks data accompanied by high CV. Laboratory comparison of field infiltrometers, namely double ring infiltrometer, Philip-Dunne infiltrometer and Mini Disk infiltrometer, on artificially prepared sandy profiles in three 208 dm

^{3}barrels, was studied by Nestingen et al. [77]. Very low CV values were determined, in average 9.1% for the Double Ring infiltrometer, 13.7% for the Philip-Dune infiltrometer and 22.7% for the Mini Disk infiltrometer. The CV values determined for Ks values in our study ranged in average between 22% (HI on NT plot) and 72% (HI on RT plot). Although the CV values are higher than those reported by Nestingen et al. [77], they are lower than values presented in studies of Ahmed et al. [74] and Olson et al. [78] reporting the averaged CV values of 168% and 91%, respectively.

#### 3.4. Mesopore and Macropore Contributions to the Total Saturated Flux

^{2}determined by MDI and 1212/m

^{2}by HI. On the other hand, there was about 1.5 times more mesopores determined by HI compared to the numbers determined by MDI. In spite of a smaller amount of macropores, their contribution to the total saturated water flux was in average 76%. Numbers of mesopores and macropores with their averaged contributions to the total saturated flux in % for each tillage treatment and each experimental phase are displayed in Figure 8. Based on the results, it can be seen that such a small device as the MDI can successfully quantify the macropore contribution to the water transport through the soil profile.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Appearance indication of the experimental fields and basic meteorological data from June 2008 until July 2009 (source: Meteorological station at the Crop Research Institute; [42]).

**Figure 2.**Comparison of K(h) data determined by Hood infiltrometer (HI) and MDI by analytical solutions suggested in the most up to date manuals.

**Figure 4.**ANOVA results for logK(h) data measured by MDI and HI on CT, RT an NT plots. NT, RT and CT are representing No-tillage, Reduced-tillage, and Conventional-tillage treatments of soil.

**Figure 5.**ANOVA results for logK(h) data measured by MDI and HI without the influence of soil treatment (data from NT only). NT is representing No-tillage treatment of soil.

**Figure 6.**Comparison of Ks data determined by HI, and MDI (upper part), with corresponding variation coefficients (lower part).

**Figure 7.**ANOVA results for logKs data determined by HI and MDI with different applied data analyses.

**Figure 8.**Upper pair of graphs describes number of macro/meso pores per 1 m

^{2}determined from MDI-Dohnal and HI data for each soil treatment (CT, RT, NT) and for each experimental phase (I-IV), lower pair of graphs describes contribution of the macro/meso pores to the total saturated flux in % with respect to the infiltrometer type, soil treatment and experimental phase.

Manual 2005 | Manual 2014 | Dohnal et al. [48] | ||||

α = 0.01 | n = 1.23 | α = 0.01 | n = 1.23 | α = 0.01 | n = 1.23 | |

Pressure head | Parameter A | Parameter A | Parameter A | |||

−5 cm | 10.1 | 9.90 | 22.5 | |||

−3 cm | 9.1 | 8.95 | 21.9 | |||

−1 cm | 8.3 | 8.09 | 21.3 | |||

Rosetta for CT | Rosetta for RT | Rosetta for NT | ||||

α = 0.0087 | n = 1.4998 | α = 0.0083 | n = 1.5089 | α = 0.0083 | n = 1.5129 | |

Pressure head | Parameter A | Parameter A | Parameter A | |||

−5 cm | 20.1 | 21.1 | 21.2 | |||

−3 cm | 19.1 | 20.1 | 20.2 | |||

−1 cm | 18.1 | 19.1 | 19.3 |

**Table 2.**Summary of the basic soil characteristics determined for the top 10 cm of the tested soil, superscript letters a, b, c indicate membership in a homogeneous group based on Fisher’s least significant difference (LSD) procedure with 95% confidence *.

Soil Treatment | Exp. Phase | Time Indication | Dry Bulk Density (g cm ^{−3}) | Particle Density (g cm ^{−3}) | Total Porosity (%) | Organic Matter Content Cox (%) |
---|---|---|---|---|---|---|

RT | I. | June 2008 | 1.27 ^{a} | 2.61 ^{a} | 51.37 ^{a} | 2.44 ^{b} |

II. | Sept. 2008 | 1.16 ^{b} | 2.63 ^{a} | 55.75 ^{a} | 2.50 ^{b} | |

III. | April 2009 | 1.21 ^{a} | 2.64 ^{a} | 54.03 ^{a} | 2.58 ^{b} | |

IV. | June 2009 | 1.26 ^{a} | 2.64 ^{a} | 52.19 ^{a} | 2.58 ^{b} | |

NT | I. | June 2008 | 1.31 ^{a} | 2.64 ^{a} | 48.46 ^{b} | 3.01 ^{c} |

II. | Sept. 2008 | 1.33 ^{a} | 2.64 ^{a} | 49.60 ^{b} | 2.67 ^{c} | |

III. | April 2009 | 1.29 ^{a} | 2.60 ^{a} | 48.39 ^{b} | 2.96 ^{c} | |

IV. | June 2009 | 1.36 ^{a} | 2.62 ^{a} | 47.98 ^{b} | 3.23 ^{c} | |

CT | I. | June 2008 | 1.26 ^{a} | 2.60 ^{a} | 51.55 ^{a} | 1.81 ^{a} |

II. | Sept. 2008 | 1.13 ^{b} | 2.61 ^{a} | 56.54 ^{a} | 1.82 ^{a} | |

III. | April 2009 | 1.27 ^{a} | 2.62 ^{a} | 52.8 ^{1a} | 1.93 ^{a} | |

IV. | June 2009 | 1.28 ^{b} | 2.61 ^{a} | 51.12 ^{a} | 1.83 ^{a} | |

Max | 1.37 | 2.64 | 57.54 | 3.24 | ||

Min | 1.13 | 2.6 | 46.98 | 1.74 | ||

Standard deviation | 0.064 | 0.012 | 3.107 | 0.464 | ||

Coefficient of variation (%) | 5.0 | 0.5 | 6.0 | 19.1 |

**Table 3.**Initial (θ

_{initial}) and final (θ

_{final}) soil moisture contents together with the resulting α and n parameters obtained by the HYDRUS 2D/3D data analysis method applied on the MDI data; coefficient of determination R

^{2}represents quality of the fit.

Exp. Phase | Treatment | θ_{initial} (cm^{3} cm^{−3}) | θ_{ifinal} (cm^{3} cm^{−3}) | α (cm^{−1}) | n (-) | R^{2} |
---|---|---|---|---|---|---|

I. | CT | 0.125 | 0.338 | 0.1397 | 2.1004 | 0.9986 |

NT | 0.157 | 0.340 | 0.2052 | 1.8914 | 0.9950 | |

RT | 0.139 | 0.342 | 0.1999 | 1.8178 | 0.9983 | |

II. | CT | 0.187 | 0.323 | 0.2190 | 1.8829 | 0.9985 |

NT | 0.222 | 0.347 | 0.6050 | 1.2315 | 0.9963 | |

RT | 0.188 | 0.339 | 0.2512 | 1.5753 | 0.9983 | |

III. | CT | 0.158 | 0.321 | 0.1627 | 1.5842 | 0.9987 |

NT | 0.195 | 0.323 | 1.0524 | 1.4240 | 0.9928 | |

RT | 0.155 | 0.338 | 0.5248 | 1.3931 | 0.9967 | |

IV. | CT | 0.234 | 0.385 | 0.5129 | 1.2259 | 0.9982 |

NT | 0.319 | 0.381 | 0.6256 | 1.1253 | 0.9926 | |

RT | 0.290 | 0.406 | 0.5060 | 1.1780 | 0.9962 |

**Table 4.**Results of Variance component analysis evaluating factors contributing to total variability in logK(h); The columns show:

^{1}decomposition of the sum of squared deviations around the grand mean,

^{2}degree of freedom associated with each sum of squares,

^{3}sums of squares divided by their degrees of freedom,

^{4}estimated variance components and

^{5}percentage of the total process variance represented by each component.

Source | Sum of Squares ^{1} | Df ^{2} | Mean Square ^{3} | Var. Comp. ^{4} | Percent ^{5} |
---|---|---|---|---|---|

TOTAL (CORRECTED) | 329.176 | 485 | |||

Infiltrometer type & Analysis | 111.561 | 4 | 27.890 | 0.2032 | 27.65 |

Tension | 81.515 | 10 | 8.151 | 0.1714 | 23.33 |

Treatment | 77.508 | 30 | 2.584 | 0.2115 | 28.78 |

Experimental phase | 38.808 | 132 | 0.294 | 0.0847 | 11.53 |

ERROR | 19.784 | 309 | 0.064 | 0.0640 | 8.71 |

**Table 5.**Overall evaluation of MDI, comparison to HI and short justification of presented data. Used scale: Very low–Low–Moderate–High–Very high.

Criteria | MDI | HI | Rationale |
---|---|---|---|

Portability | Very high | Very low | MDI with its total length of 32.7 cm and tube diameter of 3.1 cm belongs among the smallest devices enabling measurements in distant areas with limited or no source of water. |

Amount of water for infiltration | Very low | Very high | Only 95 mL can be infiltrated, and the device cannot be refilled without removal from the infiltration surface (which is possible with HI). |

Size of the infiltration area | Low | Medium | MDI offers only 16 cm^{2} of infiltration area, but thanks to its small dimensions and weight, a freshly tilled soil can sustain its weight. |

Time requirement for in-situ installation | Low | High | MDI can be ready to use relatively quickly; however, a special care needs to be paid to the infiltration surface preparation. |

Need of contact material | Moderate | Very low | Use of contact material, its type, thickness and suitability has been widely discussed (e.g., [62,63]). |

Suitability for K(h) determination | High | Very high | MDI has a limited range of pressure head settings (−0.5 to −7 cm), HI is limited by the soil bubbling point (approx. −10 cm for our tested soil), Soil Measurement Systems (USA) offer tension infiltrometers operating at pressure heads up to −30 cm, Ankeny et al. [82] presented an automated tension infiltrometer operating at pressure heads up to –50 cm. |

Suitability for Ks determination | Low | Very high | MDI does not allow infiltration at pressure head 0 cm, the Ks value can only be estimated, e.g., by extrapolation based on the K(h) values or by inverse parametrization of the infiltration data. |

Sensitivity to measurement influence by initial soil moisture content | High | Very low | MDI was proved to determine different infiltration rates for the same applied pressure head at the same soil with different initial soil moisture content (e.g., [9,58,59]). |

Affordability due to cost of the device | Very high | Low | MDI is a relatively low-cost device, when automated some additional costs are required. Interesting automated settings of 6 MDI running simultaneously at two applied pressure heads was presented by Klipa et al. [83]. |

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Báťková, K.; Miháliková, M.; Matula, S. Hydraulic Properties of a Cultivated Soil in Temperate Continental Climate Determined by Mini Disk Infiltrometer. *Water* **2020**, *12*, 843.
https://doi.org/10.3390/w12030843

**AMA Style**

Báťková K, Miháliková M, Matula S. Hydraulic Properties of a Cultivated Soil in Temperate Continental Climate Determined by Mini Disk Infiltrometer. *Water*. 2020; 12(3):843.
https://doi.org/10.3390/w12030843

**Chicago/Turabian Style**

Báťková, Kamila, Markéta Miháliková, and Svatopluk Matula. 2020. "Hydraulic Properties of a Cultivated Soil in Temperate Continental Climate Determined by Mini Disk Infiltrometer" *Water* 12, no. 3: 843.
https://doi.org/10.3390/w12030843