# Infiltration Measurements during Dry Conditions in an Urban Park in Ljubljana, Slovenia

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

## 3. Results and Discussion

#### 3.1. Infiltration Measurement Results

^{−4}to 10

^{−3}cm/s (Table 3) and is closely related to this course of experiments. ${K}_{sDRI}$ is significantly lower at T2 and T4, respectively. The discrepancy in infiltration rate between the first two replicates (D1.1 vs. D1.2 and D3.1 vs. D3.2) at T1 and T3 is also reflected in characteristically different values of ${K}_{sDRI}$, i.e., evaluation for D1.1 and D3.1 is about three times higher compared to D1.2 and D3.2. This could be attributed to several different factors.

^{−4}cm/s for the majority of measurements when A is considered according to Equation (4) (Table 3). The most uniform values with the lowest coefficient of variation (CV) of 41.7% were obtained at site T3 (Table 3), indicating a relatively high degree of soil homogeneity, while the highest CV was observed at site T2 (Table 3). However, the observed CV was significantly lower when considered for each individual location A and B within the site (T1–T4) radius. Considering results by test location (A and B) within each site, T2-A and T2-B actually exhibit the lowest CV of 13.0% and 12.5%, respectively (Table 3). This highlights the laterally variable conditions of surface soil properties over short distances (<1 m), which was also observed in the analysis of surface soil type (Table 3).

^{−3}cm/s) and sandy loam (0.5–5 × 10

^{−3}cm/s), which is consistent with the qualitative assessment of the soil texture at T1, T2, and T3. In contrast, T4 exhibits greater similarity to sandy clay loam than sandy loam.

#### 3.2. Infiltration Modeling

^{−3}cm/s using the PH model and the highest, i.e., at 0.56 × 10

^{−3}cm/s using the SP model. The PH model provided the closest match to the Ks value obtained by the Equation (1) with 0.25 × 10

^{−3}cm/s.

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 2.**Lateral infiltration of water observed during infiltration measurement using MDI at T4 (

**a**), results of K(h) using MDI at each site (T1–T4) and in-site location A and B (

**b**), and comparison of Ks for both instruments—DRI and MDI, namely selected DRI (${K}_{sDRI*}$) at each site (T1–T4) and mean ${{K}_{s}}_{MDI}$ at each site (T1–T4) and in-site location A and B (

**c**).

**Figure 3.**Comparison of infiltration rate from DRI and MDI measurements at site T2; markers represent measured data, while MDI dashed lines are extrapolated over considered time scale.

**Figure 4.**Fitted curves of Philip (PH), Horton (HO), Green-Ampt (GA), and Smith-Parlange (SP) infiltration models to the measured infiltration data at site T2: infiltration rate (

**a**) and cumulative infiltration (

**b**).

Site | Soil Texture [43] | Moisture [44] | Sun Exposure | Vegetation |
---|---|---|---|---|

T1 | sandy loam | moist | mostly shaded | dense grass |

T2 | sandy clay loam | slightly moist | sunlit | dense grass |

T3 | sandy clay loam | moist | mostly shaded | dense grass |

T4 | sandy loam | dry | sunlit | sparsely grown grass |

Infiltration Model | Infiltration Rate | |
---|---|---|

Green-Ampt | ${f}_{p}\left(t\right)={K}_{S}\left(\frac{\psi ({\theta}_{s}-{\theta}_{i})}{F\left(t\right)}+1\right)$ | (7) |

Smith-Parlange | ${f}_{p}\left(t\right)={K}_{S}+\frac{\gamma ({K}_{S}-{K}_{i})}{(\mathrm{exp}\left(\frac{\gamma F}{G({\theta}_{s}-{\theta}_{i})}\right)-1)}$ | (8) |

Horton | ${f}_{p}\left(t\right)={f}_{0}+\left({f}_{0}-{f}_{c}\right)\u2027{e}^{-kt}$ | (9) |

Philip | ${f}_{p}\left(t\right)=\frac{1}{2}S{t}^{-1/2}+c{K}_{S}$ | (10) |

Infiltration Model | Cumulative Infiltration | |

Green-Ampt | $F\left(t\right)=Kt+\psi ({\theta}_{s}-{\theta}_{i})\mathrm{l}\mathrm{n}(1+\frac{F\left(t\right)}{\psi ({\theta}_{s}-{\theta}_{i})})$ | (11) |

Smith-Parlange | $\begin{array}{c}F\left(t\right)=\left({K}_{S}-{K}_{i}\right)t\left(1-\gamma \right)+G({\theta}_{s}-{\theta}_{i})\u2027\mathrm{l}\mathrm{n}(1\\ \u2006\u2006+\frac{1}{\gamma}\left(\mathrm{exp}\left(\frac{\gamma F\left(t\right)}{G({\theta}_{s}-{\theta}_{i})}\right)-1\right))\end{array}$ | (12) |

Horton | $F\left(t\right)={f}_{c}t+\frac{({f}_{0}-{f}_{c})}{k}[1-{e}^{-kt}]$ | (13) |

Philip | $F\left(t\right)=S{t}^{1/2}+c{K}_{S}t$ | (14) |

Abbreviation | Parameter | Unit |

${f}_{p}$ | potential infiltration rate (capacity) after time of ponding ($t>{t}_{p}$) | (cm/s) |

$F$ | cumulative infiltration | (cm) |

$t$ | time | (s) |

${\theta}_{s}$ | saturated water content | (-) |

${\theta}_{i}$ | initial water content | (-) |

$\psi $ | average suction across the wetting front | (cm) |

${K}_{S}$ | saturated hydraulic conductivity | (cm/s) |

${K}_{i}$ | initial hydraulic conductivity | (cm/s) |

$G$ | capillary length scale | (cm) |

$\gamma $ | dimensionless Smith-Parlange coefficient (usually 0.8–0.85) | (-) |

$S$ | sorptivity | ($cm/{s}^{\frac{1}{2}}$) |

$c$ | soil dependent dimensionless Philip coefficient | (-) |

${f}_{0}$ | initial infiltration capacity | (cm/s) |

${f}_{c}$ | final constant infiltration rate | (cm/s) |

$k$ | Horton dimensionless coefficient that depends on the initial water content and the application rate | (-) |

Site | No. | Loc. | Soil Type | Ks_{DRI}(Equation (1)) [10 ^{−3} cm/s] | Ks_{DRI*}[10 ^{−3} cm/s] | K(h)_{MDI} (Equation (3)) [10 ^{−3} cm/s] | Ks_{MDI}(Equation (6)) [10 ^{−3} cm/s] | K(h)_{MDI}/Ks _{DRI*} | Ks_{MDI}/Ks _{DRI*} | CV of K(h)_{MDI} [%]Loc./Site | |
---|---|---|---|---|---|---|---|---|---|---|---|

T1 | D1.1 | SL | 2.99 * | 0.98 | |||||||

D1.2 | 0.98 | ||||||||||

M1.1 | T1-A | SL | 0.19 (0.05) | 1.08 | 0.19 (0.05) | 1.10 | 35.9 | 56.2 | |||

M1.3 | 0.22 (0.05) | 1.22 | 0.22 (0.05) | 1.24 | |||||||

M1.4 | 0.37 (0.09) | 2.15 | 0.38 (0.09) | 2.18 | |||||||

M1.2 | T1-B | SL | 0.61 (0.15) | 3.37 | 0.62 (0.15) | 3.42 | 28.1 | ||||

M1.5 | 0.88 (0.21) | 5.18 | 0.90 (0.21) | 5.26 | |||||||

M1.6 | 0.52 (0.12) | 3.06 | 0.53 (0.12) | 3.11 | |||||||

T2 | D2.1 | SCL | 0.25 | 0.25 | |||||||

M2.1 | T2-A | CL | 0.39 (0.16) | 3.88 | 1.56 (0.64) | 15.35 | 13.0 | 60.1 | |||

M2.2 | 0.44 (0.18) | 4.42 | 1.76 (0.72) | 17.48 | |||||||

M2.5 | 0.34 (0.14) | 3.40 | 1.36 (0.56) | 13.45 | |||||||

M2.3 | T2-B | SCL | 0.13 (0.04) | 0.89 | 0.52 (0.16) | 3.51 | 12.5 | ||||

M2.4 | 0.13 (0.03) | 0.81 | 0.52 (0.12) | 3.20 | |||||||

M2.6 | 0.10 (0.03) | 0.65 | 0.40 (0.12) | 2.55 | |||||||

T3 | D3.1 | SCL | 2.39 * | 0.97 | |||||||

D3.2 | 0.83 | ||||||||||

D3.3 | 1.10 | ||||||||||

M3.1 | T3-A | SCL | 0.17 (0.04) | 1.06 | 0.18 (0.04) | 1.10 | 18.9 | 41.7 | |||

M3.2 | 0.23 (0.03) | 0.70 | 0.24 (0.03) | 0.73 | |||||||

M3.4 | 0.17 (0.04) | 1.09 | 0.18 (0.04) | 1.13 | |||||||

M3.3 | T3-B | SCL | 0.44 (0.05) | 1.34 | 0.45 (0.05) | 1.39 | 34.7 | ||||

M3.5 | 0.21 (0.06) | 1.35 | 0.22 (0.06) | 1.40 | |||||||

M3.6 | 0.34 (0.09) | 2.18 | 0.35 (0.09) | 2.26 | |||||||

T4 | D4.1 | SL | 0.18 | 0.30 | |||||||

D4.2 | 0.41 | ||||||||||

M4.1 | T4-A | SL | 0.79 (0.19) | 4.56 | 2.63 (0.63) | 15.26 | 27.7 | 42.6 | |||

M4.2 | 1.18 (0.28) | 6.95 | 3.93 (0.93) | 23.26 | |||||||

M4.5 | 0.72 (0.17) | 4.46 | 2.40 (0.57) | 14.93 | |||||||

M4.3 | T4-B | SL | 0.45 (0.11) | 2.65 | 1.50 (0.37) | 8.87 | 18.2 | ||||

M4.4 | 0.55 (0.13) | 3.28 | 1.83 (0.43) | 10.98 | |||||||

M4.6 | 0.38 (0.09) | 2.25 | 1.27 (0.30) | 7.53 |

_{DRI*}: Selected Ks value from DRI at the considered site; columns K(h)

_{MDI}and K(h)

_{MDI}/Ks

_{DRI*}: first value considers A according to Equation (4), the second value in parentheses considers A according to Equation (5); CV: Coefficient of variation [%] that considers the first value in K(h)

_{MDI}column.

**Table 4.**The optimal fit of parameters of Philip (PH), Green-Ampt (GA), and Smith-Parlange (SP) infiltration models.

Parameter | Green-Ampt | Smith-Parlange | Philip |
---|---|---|---|

${K}_{S}({10}^{-3}\mathrm{c}\mathrm{m}/\mathrm{s})$ | 0.42 (0.39–0.44) | 0.56 (0.53–0.58) | 0.33 (0.14–0.42) |

${\theta}_{s}-{\theta}_{i}(-)$ | 0.27 (0.27–0.45) | 0.29 (0.28–0.41) | / |

$\psi \left(\mathrm{c}\mathrm{m}\right)$ | 8.5 (4.5–9.5) | / | / |

$G\left(\mathrm{c}\mathrm{m}\right)$ | / | 5.0 (5.0–7.0) | / |

${K}_{i}({10}^{-3}\mathrm{c}\mathrm{m}/\mathrm{s})$ | / | 0.022 (0.008–0.025) | / |

$S({10}^{-3}\mathrm{c}\mathrm{m}/{\mathrm{s}}^{1/2})$ | / | / | 0.69 (0.58–0.86) |

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## Share and Cite

**MDPI and ACS Style**

Svetina, J.; Prestor, J.; Šraj, M.
Infiltration Measurements during Dry Conditions in an Urban Park in Ljubljana, Slovenia. *Water* **2023**, *15*, 3635.
https://doi.org/10.3390/w15203635

**AMA Style**

Svetina J, Prestor J, Šraj M.
Infiltration Measurements during Dry Conditions in an Urban Park in Ljubljana, Slovenia. *Water*. 2023; 15(20):3635.
https://doi.org/10.3390/w15203635

**Chicago/Turabian Style**

Svetina, Janja, Joerg Prestor, and Mojca Šraj.
2023. "Infiltration Measurements during Dry Conditions in an Urban Park in Ljubljana, Slovenia" *Water* 15, no. 20: 3635.
https://doi.org/10.3390/w15203635