# Automated Laboratory Infiltrometer to Estimate Saturated Hydraulic Conductivity Using an Arduino Microcontroller Board

^{*}

## Abstract

**:**

^{2}= 0.9826 and r-RSME = 0.94%).

## 1. Introduction

^{3}y

^{−1}[2]. This condition has several negative effects such as saline water intrusion to aquifers in coastal regions, affectations to rivers, springs and wetlands that depend on groundwater supplies, land subsidence due to pore pressure reductions [3,4] and climate changes [2]. In order to achieve an adequate planning and management of groundwater, it is necessary to improve the knowledge of its functioning; the proper understanding of groundwater flow systems is of paramount importance for hydrogeologists.

## 2. Materials and Methods

#### 2.1. The Automated Laboratory Infiltrometer

^{−1}K

^{−1}) to insulate it from the environment. Its lower end is connected to a plastic funnel and a clear hose to drain out the water; to keep the lower hydraulic head constant, the hose is connected to a small tank from the bottom and once it reaches the desired level it is drained trough the upper outlet to the container of the digital scale.

^{−3}m [36] is installed on the top of the container B to measure infiltration volumes. A generic 10 kg load cell (accuracy of ±0.05% [37]) connected to an amplifier module HX711 is used to measure drained water mass.

#### 2.2. Data Acquisition System

#### 2.3. Drained Water Flux Rates Measurement

^{3}), ${m}_{w}$ is the mass (kg) and ${\rho}_{w}$ density (kg m

^{−3}) of the water. These data are used to calculate the drained water rate ($Q$) per time unit (m

^{3}h

^{−1}). Finally, the water flux rates $q$ (m h

^{−1}) are determined by Equation (1), where $A$ is the cross-sectional area of the column (m

^{2}),

^{−4}kg and cv = 0.11%; the upper limit (UL) is the sum of 2σ and the mean; the lower limit (LL) is the result of the mean minus 2σ. A pre-processing step was done by taking 20 samples at time, then the data were filtered extracting the median, which is more robust than the mean in presence of outliers or skewed data.

#### 2.4. Water Flux Rates Determination by Measuring Infiltration Rates

_{1}) quasi-constant. This level is maintained by the use of a float level switch with a range of 5.0 × 10

^{−3}m; once the water reaches its lower level (h

_{1}-5.0 × 10

^{−3}m), a water pump submerged in the container B is activated until the level reaches the upper level (h

_{1}). The infiltration rate is measured in container B by the use of an ultrasonic ranging module HC-SR04. Basically, its transmitter emits a 40 KHz ultrasonic wave when it is triggered and a timer is started. An ultrasonic pulse travels outward until it encounters an object (in this case water), the water reflects back the pulse, the ultrasonic receiver detects the reflected wave and stops the timer; this is the traveling time, which divided by two and multiplied by the sound speed, gives the distance between the sensor and the water. The increase of this distance multiplied by the cross-sectional area of the container B gives the infiltrated volume, which is accumulated per hours and considered the infiltration rate per time unit (m h

^{−1}). The water flux rates are determined by Equation (1).

^{−4}m and cv equal to 0.23%; the upper limit (UL) is the sum of 2σ and the mean; the lower limit is the result of the mean minus 2σ. A pre-processing step was done by taking 20 samples at a time, then the data were filtered extracting the median.

#### 2.5. Low Pass Filter

#### 2.6. Water Flux Rates Determination by Using Temperature Time Series

#### 2.6.1. The Heat and Fluid Transport Equation

^{−1}°C

^{−1}), $T$ is the temperature (°C), $q$ is the infiltration flux (m s

^{−1}), ${C}_{w}$ and ${C}_{s}$ are the volumetric heat capacity of the water and soil porous media respectively (J m

^{−3}°C

^{−1}), $z$ is the distance along the vertical axis (m) and $t$ is the elapsed time (s). There are some analytical solutions proposed for (3) in the scientific literature; the reader can refer to Irvine et al. [30] for a detailed review. The proposal by Hatch et al. [39] is one of the most commonly used to calculate water flux rates through porous media by using either the amplitude (4) or phase differences (5) of a periodic temperature signal between two points at different depths. This model assumes a quasi-sinusoidal temperature oscillation at the upper boundary and one directional water flow path.

^{2}s

^{−1}), ${A}_{r}$ and $\Delta t$ are the amplitude and phase relations (dimensionless), $v$ is the water front velocity (m s

^{−1}), $P$ is the period of the sinusoidal signal (s), ${\lambda}_{0}$ is the baseline thermal conductivity of the saturated sediment (J s

^{−1}m

^{−1}°C

^{−1}), $\beta $ is the thermal dispersivity (m), ${v}_{f}$ is the linear particle velocity (m s

^{−1}) and ${n}_{e}$ is the effective porosity (dimensionless). Both ${A}_{r}$ and $\Delta t$ are less influenced by errors in thermal conductivity at higher flow rates, as expected when advection becomes more important for heat transport [40]. As demonstrated by Stallman [41], analysis of diurnal temperature fluctuations may yield accurate detection of velocity to a minimum of 0.3 cm/day, so it is useful for most of the soil textures.

#### 2.6.2. Dynamic Harmonic Regression (DHR)

#### 2.6.3. Temperature Time Series Processing

#### 2.6.4. Soil Sample Preparation

#### 2.7. Saturated Hydraulic Conductivity

^{−1}), ${K}_{s}$ (m s

^{−1}) is the saturated hydraulic conductivity and $dh/dl$ is the hydraulic gradient (dimensionless); the negative sign indicates that the flow of water is in the direction of decreasing head.

## 3. Results

#### 3.1. Hydraulic Boundary Conditions and Data Processing

^{−3}m) at the top boundary and free drainage and a constant hydraulic head at the bottom boundary (0.45 m). Infiltration rates and drained rates were filtered by using a low pass filter; water flux rates were determined and fitted using a MATLAB polynomial fitting.

#### 3.2. Temperature Boundary Conditions and Data Processing

#### 3.3. Water Flux Rates Comparison

^{2}) and relative root mean square error (r-RSME) are also shown.

^{2}expresses the correlation between the measured values and the estimated ones; the best approximation corresponds to the highest R

^{2}(closer to 1), RMSE shows the difference between the measured values and the predicted ones; it indicates the scattering of data around a straight line inclined 45°. The approximation is better if RMSE is minimal (tends to 0). Normalized root means square error (nRSME) or relative root mean square error (r-RSME) is calculated by dividing RMSE with the average value of measured data. According to Despotovic et al. [46], model accuracy is considered excellent when r-RMSE is less than 10%, good if 10% < r-RMSE < 20%, fair if 20% < r-RMSE < 30%, and poor if r-RMSE > 30%. Therefore, an excellent correlation among the methods was found, which indicates that the developed device (ALI) is able to estimate efficiently water flux rates by three different methods, giving more confidence in its results.

#### 3.4. Determination of Saturated Hydraulic Conductivity

_{1}= 2.05 m, h

_{2}= 0.45 m, dl = 1.0 m and the water flux rates in steady state conditions from each of the three approaches. On average, the saturated hydraulic conductivity was 8.61 × 10

^{−5}m s

^{−1}, which is within the range of the values reported on the saturated hydraulic conductivity in relation to the soil texture table from the U.S. Department of Agriculture (USDA) [47] which gives a range of 4.2 × 10

^{−5}to 1.41 × 10

^{−4}m s

^{−1}for soils with sand textures. Table 2 shows the average Ks from the three approaches.

## 4. Conclusions

^{2}= 0.9826 and r-RSME = 0.94% between Infiltrated and Hatch; R

^{2}= 0.9857 and r-RSME = 0.12% among Hatch and Drained; and R

^{2}= 0.9826 and r-RSME = 0.94% between Infiltrated and Drained). The saturated hydraulic conductivity determined for the three methods falls inside the ranges established by the USDA for the analyzed soil, which proved its efficiency.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 4.**Raw temperature time series from eight sensors installed at different depths and sampled every 5 min.

**Figure 5.**Resampled temperature time series from eight sensors, sampling rate was reduced to 48 samples per fundamental cycle. There is still some noise on the crests and troughs. Phase delays can be observed, amplitude ratios are not so observable due to the proximity between the temperature sensors.

**Figure 6.**Resampled and filtered temperature time series. A low-pass FIR filter was used to remove high-frequency noise and Dynamic Harmonic Regression (DHR) to remove the long-term trend. Only the changes in amplitude due to artificially induced heating cycles remain.

**Figure 7.**Comparison of water flux rates determined by three approaches. There is a trend to start with higher q values and then the curves tend to stabilize. A high similarity among the curves can be observed once the steady state has been reached.

**Table 1.**Physical and thermal parameters of the soil and water used for water flux rates calculation by using analytical solution for heat and transport Equation (3).

Parameters | Determined | Units |
---|---|---|

Effective porosity (${n}_{e}$) | 0.28 | dimensionless |

Volumetric heat capacity of soil (${C}_{s}$) | 0.5 | Cal cm^{−3} °C^{−1} |

Volumetric heat capacity of water (${C}_{w}$) | 1.0 | Cal cm^{−3} °C^{−1} |

Thermal dispersivity ($\beta $) | 0.001 | M |

Baseline thermal conductivity (${\lambda}_{0}$) | 0.0045 | Cal s^{−1} cm^{−1} °C^{−1} |

**Table 2.**Average saturated hydraulic conductivity determined for the three approaches and range of values reported by the U.S. Department of Agriculture (USDA) for sand texture soils.

Approach | Ks | Units |
---|---|---|

Heat as a tracer ^{a} | 8.6318 × 10^{−5} | m s^{−1} |

Infiltrated ^{b} | 8.6384 × 10^{−5} | m s^{−1} |

Drained ^{c} | 8.5680 × 10^{−5} | m s^{−1} |

USDA ^{d} | 4.2 × 10^{−5} to 1.41 × 10^{−4} | m s^{−1} |

^{a}Ks determined using heat as tracer and the analytical solution from Hatch et al. [39].

^{b}Ks determined by measuring infiltration rates from the top.

^{c}Ks determined by measuring drained flux rates from the bottom.

^{d}Ranges of values of Ks for soils with sand texture reported by the USDA [47].

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## Share and Cite

**MDPI and ACS Style**

Rodríguez-Juárez, P.; Júnez-Ferreira, H.E.; González Trinidad, J.; Zavala, M.; Burnes-Rudecino, S.; Bautista-Capetillo, C.
Automated Laboratory Infiltrometer to Estimate Saturated Hydraulic Conductivity Using an Arduino Microcontroller Board. *Water* **2018**, *10*, 1867.
https://doi.org/10.3390/w10121867

**AMA Style**

Rodríguez-Juárez P, Júnez-Ferreira HE, González Trinidad J, Zavala M, Burnes-Rudecino S, Bautista-Capetillo C.
Automated Laboratory Infiltrometer to Estimate Saturated Hydraulic Conductivity Using an Arduino Microcontroller Board. *Water*. 2018; 10(12):1867.
https://doi.org/10.3390/w10121867

**Chicago/Turabian Style**

Rodríguez-Juárez, Pedro, Hugo E. Júnez-Ferreira, Julián González Trinidad, Manuel Zavala, Susana Burnes-Rudecino, and Carlos Bautista-Capetillo.
2018. "Automated Laboratory Infiltrometer to Estimate Saturated Hydraulic Conductivity Using an Arduino Microcontroller Board" *Water* 10, no. 12: 1867.
https://doi.org/10.3390/w10121867