# Influence of Rainfall Events and Surface Inclination on Overland and Subsurface Runoff Formation on Low-Permeable Soil

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research on Geotechnical Properties

^{−3}[60]. The compaction characteristics of a soil can be assessed by means of standard laboratory tests. In the Proctor test, the volume of the mold is 1 dm

^{3}and the soil is compacted by a rammer consisting of a 2.5 kg mass falling freely through 320 mm. The soil is compacted in three equal layers, with each layer receiving 25 blows with the rammer for at least five soil samples. After compaction, the bulk density and water content of the soil are determined and the dry density calculated.

_{S}= 0.88, 0.92, 0.95, or 1.00, which corresponds to a soil porosity n = 0.40, 0.38, 0.35, or 0.32, respectively. The determination of the filtration coefficient was also carried out with the use of a Saturo infiltrometer (dual head) (METER Group, Pullman, DC, USA) (Figure 1). In this case, the tests were performed on samples formed in the cylinder of a medium-sized Proctor apparatus (Wille Geotechnik, Germany) with a diameter of 25 cm and a height of 20 cm at a moisture content of 10% until a compaction index of I

_{S}= 0.88 (n = 0.40) was obtained. The filtration coefficient from the infiltrometer tests was determined using a ring with a diameter of 14.4 cm stuck into the soil sample to a depth of 5 cm. The test was performed in duplicate with two and three measurement cycles.

#### 2.2. Surface and Subsurface Runoff Studies

^{−3}, which allowed us to obtain a soil compaction index of I

_{S}= 0.87. This index corresponds to a soil porosity of n = 0.40, which falls within the range of silty soil porosity given by Kaczyński [61] for upland and mountain areas of southern Poland. For each series, three precipitation simulations were performed, during which the simulator operated for 40 min. As part of the research, 30 mm rainfall was generated for a duration of 40 min, which corresponds to a rainfall intensity of 0.75 mm·min

^{−1}. According to Lambor [62], for an area with an annual precipitation of 700 mm, this intensity is characterized by a probability of about 5–10%, which corresponds to the probability for which road drainage devices are designed [63]. According to the Institute of Meteorology and Water Management–National Research Institute [64], rainfall of 30 mm is considered critical, leading to rising water in water courses and the start of surface runoff.

#### 2.3. Monitoring of the Infiltration Process Using the EIS Method

#### 2.4. Calculations of Overland and Subsurface Runoff with the Use of Models Taking into Account the Infiltration Process

_{x}(m·s

^{−1}) is the hydraulic conductivity of the soil in the x-direction, k

_{z}(m·s

^{−1}) is the hydraulic conductivity of the soil in the z-direction, H (m) is the water total head, and Q (m·s

^{−1}) is the boundary flux.

_{s}(m·s

^{−1}) is the hydraulic conductivity of a soil, given as half of the value of the soil coefficient of permeability [66]; i (-) is the hydraulic gradient; H

_{p}(m) is the height of ponding, often assumed to be equal to 0, because surface ponding triggers overland runoff; z

_{f}(m) is the depth of the wetting front location; and ψ

_{f}(m) is the weight of soil suction pressure at the base of the wetting front.

_{a}(%) is the sand fraction content, and Cl (%) is the clay fraction content. The equation is easy to calculate and there is no need for information on the soil water characteristic curve (retention curve).

_{r}(-) is the degree of soil saturation.

_{p}). After this, the overland runoff begins, and the amount of water accumulated (F) in the soil profile can be calculated from the following relationship:

_{p}(mm) is the accumulation of rainwater in the soil at the moment of ponding of the soil surface, θ

_{s}(-) is the soil moisture content at full saturation, and θ

_{i}(-) is the soil moisture content before rainfall.

^{−6}m·s

^{−1}were adopted from the Saturo infiltrometer tests, and the retention characteristics were determined using the retention parameters proposed by the SEEP/W program for silty soils.

#### 2.5. Estimation of Overland and Subsurface Runoff Using the MSME Model

_{a}), and vice versa. The antecedent moisture content is given as follows:

_{Qsubs}) was calculated using the following equations:

_{a1}(mm) is the initial abstraction for subsurface runoff, PET5 (mm) is the sum of five days’ potential evapotranspiration computed using the Penman–Monteith method, S

_{a}(mm) is the maximum potential retention for the area where subsurface runoff occurs, and a (-) is the coefficient for the proportion of area with saturated soil.

_{Qsurf}) was calculated using the following equations:

_{a2}(mm) is the initial abstraction for overland runoff, S

_{b}(mm) is the maximum potential retention for the area where overland runoff occurs, and CN (-) is the curve number (CN) parameter.

_{obs,i}(mm) is the observed direct runoff, Q

_{calc,i}(mm) is the calculated direct runoff, ${\overline{Q}}_{obs,i}$ (mm) is the mean value of the observed direct runoff values, and N (-) is the number of observations.

## 3. Results of Studies

#### 3.1. Geotechnical Properties of Soil

^{−3}at the optimum moisture content of 13.4%.

_{S}= 0.88 to 0.99 (decreased porosity from 0.41 to 0.32), and ranged from 4.31 × 10

^{−7}to 1.11 × 10

^{−8}m·s

^{−1}, respectively (Figure 6). On the other hand, the coarse clay silt coefficient of permeability determined with the Saturo infiltrometer (Figure 7), when the porosity value is 0.41, corresponding to the compaction index of I

_{S}= 0.88, was on average 4.92 × 10

^{−6}m·s

^{−1}. The obtained values indicate that the tested soil may be classified as poorly or semipermeable [75].

_{S}= 0.88, obtained from the oedometer and infiltrometer tests, showed that the oedometer value was an order of magnitude lower than that obtained from the infiltrometer tests. These differences may be due to the size of the samples and the test method. Taking into account the different values of the coefficient of permeability (filtration), calculations of the overland and subsurface runoff were conducted for four values of this coefficient. One of them (the lowest) was the average value of the oedometer tests for the sample with a compaction index of I

_{S}= 0.88, so the porosity was n = 0.40 (k = 5.0 × 10

^{−7}m·s

^{−1}). The next two values (k = 4.0 × 10

^{−6}and 2.0 × 10

^{−6}m·s

^{−1}) were adopted from the Saturo infiltrometer tests. These values corresponded to the range of values of the infiltration rate when tests were approaching the end. The last value of the coefficient of permeability (k = 1.0 × 10

^{−6}m·s

^{−1}) was adopted as a geometric mean of the parameter derived from the two methods used.

#### 3.2. Overland and Subsurface Runoff

^{−1}for slopes of 2.5 and 5.0%, respectively. For this rainfall episode, no subsurface runoff was observed (Figure 9). Before the research started, the soil was characterized by a relatively low moisture content, and therefore also a high value of moisture content deficit and, at the same time, high capacity. As a result of rainfall, most of the moisture was retained in the soil, increasing its moisture content before the next rainfall event. This was confirmed by the soil moisture content measurement results, determined before the second rainfall episode, which increased by 2.5- and 2.2-fold for runoff surface slopes of 2.5 and 5.0%, respectively (Table 1). The results of the degree of soil saturation (the ratio of water volume in the soil to the pore volume) calculations indicate that it increased from 0.39 to 0.71–0.72 after the first rainfall episode. Theoretical calculations of soil moisture content showed that the maximum moisture content of soil is 26.1%, and the results of determinations of this parameter in the subsurface part of the soil sample showed that the degree of saturation was slightly higher (0.82–0.93).

^{−1}in the second rainfall episode and 0.58 and 0.68 mm·min

^{−1}in the third episode, for a runoff surface slope of 2.5 and 5.0%, respectively. It is noticeable that the maximum values of the runoff intensity in the third rainfall episode were slightly lower than the rainfall intensity (0.75 mm·min

^{−1}).

^{−1}. It should, however, be noted that, in the case of the second rainfall episode, the subsurface runoff occurred only after the end of the rainfall. In the case of the model with a 5.0% slope, subsurface runoff was observed only in the third rainfall episode. At the peak, its intensity was twice as high as that measured for the runoff in the model with a lower inclination of the soil surface and was 0.025 mm·min

^{−1}. Lack of subsurface runoff in the first episode at both slopes may result from the lowest initial soil moisture, which in the case of cohesive soils means that rainfall reaching the soil surface does not seep but forms a layer of flowing water. This is related to the aggregation of soil particles and clogging of its pores. Laboratory studies by Morbidelli et al. [76] led to similar conclusions, i.e., that in sloping bare soils, overland runoff is formed even when the rainfall intensity is smaller than the saturated hydraulic conductivity.

#### 3.3. Monitoring of Water Infiltration within the Soil

#### 3.4. Verification of Calculation Models

#### 3.4.1. Green–Ampt and Richards Models

^{−6}m·s

^{−1}. The value of the EF parameter (Table 3) for the model with a 2.5% inclination was 0.77–0.80 in the Green–Ampt and Richards method, respectively, and 0.95–0.96 for the model with a 5.0% inclination of the ground surface. On the other hand, acceptable EF values (0.64–0.79) were obtained for the model with a surface inclination of 5% for the two highest values of the coefficient of permeability. This is taking into account that, in the analyzed cases, overland runoff dominated, so the results of the calculations were used for further analyses, with a coefficient of permeability of 2.10 × 10

^{−6}m·s

^{−1}.

#### 3.4.2. MSME Model (Verification of Suitability for the Total Runoff Estimation)

_{a}and S

_{b}retention parameters were significantly lower for soil with a 5.0% slope in comparison to a 2.5% slope. It is related, as in the case of the CN parameter, to a lower water retention capacity in soils with a higher slope of the runoff surface, which was confirmed in this study. As a consequence, the initial losses of I

_{a1}parameter for subsurface runoff and I

_{a2}parameter for overland runoff were also reduced.

#### 3.5. Discussion

^{−1}, and the value of the coefficient of permeability was estimated at 0.12 mm·min

^{−1}. In the case of less permeable soil, one should expect a higher value of overland runoff.

## 4. Conclusions

_{surf}) and subsurface runoff (Q

_{subsr}) of impermeable soils, and its quality is comparable to that of the Green–Ampt and Richards models. The Green–Ampt and Richards method are based on physical assumptions and soil properties, but the simple empirical model MSME has parameters that are optimized based on observed rainfall–runoff events. This may be the main reason why the results of the MSME model are slightly better than those achieved by physical approaches. A limitation of the MMSE model in relation to the physical models is the inability to determine the course of infiltration over time and the need to calibrate the parameters based on the observed rainfall–runoff episodes. However, since it is a simple empirical model, it can be used by hydrologists to estimate the runoff in catchments. So, it is necessary to conduct further research on the application of this model on a real scale in various catchments to prove its usefulness in engineering calculations. Also, the authors will consider performing a study on the influence of artificial drainage on runoff formation and would include these results in the analyzed models. In a real catchment, the use of modern technique, like satellite imagines will be considered to indirectly assess soil moisture and link them with the parameters of the MSME model.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**General view of Saturo infiltrometer (dual head) (

**a**) and model of soil permeability testing by the infiltration method (

**b**).

**Figure 6.**Changes in the coarse clay coefficient of permeability over time (

**a**) and depending on the porosity/compaction index (

**b**).

**Figure 7.**Time dependence of the coarse clay coefficient of permeability in the Saturo infiltrometer tests.

**Figure 8.**Changes in overland runoff during rainfall simulation in measurement series (rainfall episodes).

**Figure 9.**Changes in subsurface runoff during rainfall simulation in measurement series (rainfall episodes).

**Figure 10.**Changes in soil resistance during three rainfall episodes at a 2.5% inclination of the soil surface.

**Figure 11.**Changes in soil resistance during three rainfall episodes at a 5.0% inclination of the soil surface.

**Figure 12.**Dependence of overland runoff on the duration of a rainfall episode: comparison of the results of measurements and calculations using the Green–Ampt method.

**Figure 13.**The results of overland and subsurface runoff calculations for the model with a soil surface inclination of 2.5%.

**Figure 14.**The results of overland and subsurface runoff calculations for the model with soil surface inclination of 5.0%.

Runoff Slope (%) | Rainfall Episode | Precipitation | Soil Moisture Content ^{(1)} before Rainfall(%) | Volumetric Soil Moisture Content ^{(2)} before/afterthe Examination (-) | Runoff Record | |||
---|---|---|---|---|---|---|---|---|

Height (mm) | Duration (min) | Intensity (mm·min ^{−1}) | Overland | Subsurface | ||||

2.5 | 1 | 30 | 40 | 0.75 | 10.0 | 0.39/0.72 | yes | no |

2 | 24.2 | 0.72/0.92 | yes | yes | ||||

3 | 26.4 | 0.81/0.94 | yes | yes | ||||

5.0 | 1 | 10.0 | 0.39/0.71 | yes | no | |||

2 | 21.5 | 0.71/0.90 | yes | no | ||||

3 | 23.0 | 0.87/0.97 | yes | yes |

^{(1)}value from the examination,

^{(2)}value calculated from the water balance.

Number of the Rainfall Episode | Type of Runoff | Soil Coefficient of Permeability Used in the Calculations (m·s^{−1}) | Inclination of Soil Surface | |||||
---|---|---|---|---|---|---|---|---|

2.5% | 5.0% | |||||||

Observations | Model | Observations | Model | |||||

Green–Ampt | Richards | Green–Ampt | Richards | |||||

Runoff Value (mm) | ||||||||

1 | overland | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 0.61 | 0.00 3.02 9.76 15.49 | 0.96 1.32 6.85 12.96 | 2.03 | 0.00 3.02 9.76 15.49 | 0.20 0.88 6.76 12.91 |

subsurface | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{-7} | 0.00 | - | 0.00 0.00 0.00 0.00 | 0.0 | - | 0.00 0.00 0.00 0.00 | |

2 | overland | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 16.11 | 6.83 14.24 19.37 22.78 | 7.38 8.33 14.46 19.32 | 14.15 | 6.10 13.59 18.87 22.41 | 8.25 8.95 15.27 19.91 |

subsurface | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 0.39 | - | 0.19 0.00 0.00 0.00 | 0.0 | - | 0.56 0.19 0.00 0.00 | |

3 | overland | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 25.17 | 11.23 17.94 22.14 24.78 | 28.25 28.36 18.14 18.01 | 26.78 | 14.61 20.60 24.10 26.20 | 28.11 28.31 17.88 18.00 |

subsurface | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 0.75 | - | 0.90 0.77 0.00 0.00 | 1.53 | - | 1.42 0.77 0.00 0.00 | |

Total | overland | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 43.72 | 18.1 35.2 51.3 63.1 | 36.59 38.00 39.46 50.29 | 42.96 | 20.71 37.21 52.73 64.10 | 36.56 38.14 39.91 50.82 |

subsurface | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 5.20 | - | 1.49 0.91 0.00 0.00 | 2.66 | - | 2.42 0.78 0.00 0.00 |

**Table 3.**Values of metrics—RMSE and Nash–Sutcliffe EF [70].

Type of Runoff | Soil Coefficient of Permeability Used in the Calculations (m^{.}s^{−1}) | Inclination of Soil Surface | |||
---|---|---|---|---|---|

2.5% | 5.0% | ||||

Model | Model | ||||

Green–Ampt | Richards | Green–Ampt | Richards | ||

Root Mean Square Error, RMSE (mm) (Equation (21)) | |||||

overland | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 162.15 35.38 59.77 153.62 | 49.50 41.10 52.57 123.60 | 125.29 22.79 51.50 144.27 | 23.07 17.70 59.35 132.08 |

subsurface | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | - | 0.25 0.30 0.63 0.63 | - | 0.19 0.33 1.35 1.35 |

Modeling efficiency, EF [-] (Equation (22)) | |||||

overland | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | 0.09 0.80 0.66 0.14 | 0.72 0.77 0.70 0.31 | 0.74 0.95 0.89 0.70 | 0.95 0.96 0.87 0.72 |

subsurface | 4.0 × 10^{−6}2.0 × 10 ^{−6}1.0 × 10 ^{−6}5.0 × 10 ^{−7} | - | −0.54 −0.86 −2.86 −2.86 | - | 0.79 0.64 −0.50 −0.50 |

Slope Inclination | Q_{surfobs} | Q_{subsurfobs} | Q_{totobs} | Q_{surcalc} | Q_{subsurfcalc} | Q_{totcalc} | CN | M | S_{a} | S_{b} | I_{a1} | I_{a2} |
---|---|---|---|---|---|---|---|---|---|---|---|---|

- | mm | - | mm | |||||||||

2.5 | 10.8 | 0.40 | 11.16 | 11.19 | 0.21 | 11.40 | 89.7 | 0.00 | 27.1 | 787.1 | 22.9 | 122.6 |

5.0 | 12.1 | 0.47 | 12.53 | 11.91 | 0.59 | 12.51 | 93.0 | 0.00 | 18.2 | 654.7 | 16.5 | 62.2 |

_{surfobs}is the observed overland runoff, Q

_{subsurfobs}is the observed subsurface runoff, Q

_{totobs}is the observed total runoff (sum of overland and subsurface runoff), Q

_{surfcalc}is the calculated observed overland runoff, Q

_{subsurfcal}is the calculated observed subsurface runoff, Q

_{totcalc}is the calculated total runoff (sum of overland and subsurface runoff), I

_{a1}is the initial abstraction for subsurface runoff, M is the antecedent moisture content, S

_{a}is the maximum potential retention for the area where subsurface runoff occurs, I

_{a2}is the initial abstraction for overland runoff (in mm), S

_{b}is the maximum potential retention for the area where overland runoff occurs (mm), and CN is the calculated curve number.

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**MDPI and ACS Style**

Gruchot, A.; Zydroń, T.; Wałęga, A.; Pařílková, J.; Stanisz, J.
Influence of Rainfall Events and Surface Inclination on Overland and Subsurface Runoff Formation on Low-Permeable Soil. *Sustainability* **2022**, *14*, 4962.
https://doi.org/10.3390/su14094962

**AMA Style**

Gruchot A, Zydroń T, Wałęga A, Pařílková J, Stanisz J.
Influence of Rainfall Events and Surface Inclination on Overland and Subsurface Runoff Formation on Low-Permeable Soil. *Sustainability*. 2022; 14(9):4962.
https://doi.org/10.3390/su14094962

**Chicago/Turabian Style**

Gruchot, Andrzej, Tymoteusz Zydroń, Andrzej Wałęga, Jana Pařílková, and Jacek Stanisz.
2022. "Influence of Rainfall Events and Surface Inclination on Overland and Subsurface Runoff Formation on Low-Permeable Soil" *Sustainability* 14, no. 9: 4962.
https://doi.org/10.3390/su14094962