# Methods of In Situ Assessment of Infiltration Rate Reduction in Groundwater Recharge Basins

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

^{−5}m/s). The observation points are distributed within two layers at 0.28 m and 0.68 m depth. The lab scale experiment features an electronic scale in the outflow to control the percolation volumes, whereas in the fields scale, the lower boundary of the infiltration unit is directly connected with the unsaturated zone of the site. Infiltrated water was from the Elbe river and was mixed with sodium chloride (NaCl) for tracer experiments. River water (DOC ≈ 5 mg/L; TSS ≈ 20 mg/L) was pumped into the infiltration basins with an annual hydraulic loading rate of 300 m/a under wet:dry cycles of 1:3 (24 h infiltration followed by 72 h dry period). This designed hydraulic loading rate represents the recharge of a 300 m high water column with an area of 1 m

^{2}within one year. In total, nine infiltration cycles, which were equivalent to a total specific volume of nearly 29,000 L/m

^{2}, were run. Tracer experiments were performed which introduced NaCl at a concentration of 1 g/L into the river water in the first six hours of each infiltration cycle, to determine the time for solute transport by way of a installed monitoring sensor, located 28 cm below the flooding-basin floor. The frequency domain reflectometry (FDR) sensor measures volumetric water content (vol%), electrical conductivity (mS/cm), and temperature (°C) at two minutes intervals. Further details of the infiltration setup and description of the measuring sensors are presented by Fichtner et al. [19].

#### 2.1. Tracer Method

_{50}/v

_{50o}(fraction of linear velocity based on time t

_{50}over the initial linear velocity in the first infiltration cycle) in Equation (1), is calculated with the time it takes to reach the half of the maximum rise of electrical conductivity (t

_{50}) at the depth to the sensor (z) [30]. The monitored changes of v

_{50}/v

_{50o}in the infiltration experiment can be interpreted as the reduction of the infiltration rate of the medium.

#### 2.2. Libardi Method

_{o}):

_{L}and B

_{L}at depth L (Figure 2), by integrating the Richard’s equation from soil surface (z = 0) down to depth z = L, the hydraulic conductivity can be calculated (see Equation (3)). A

_{L}is represented by the inverse of the slope γ, whereas B

_{L}is the multiplication of A

_{L}with the natural logarithm of the fraction of slope γ times initial hydraulic conductivity (Ko) over parameter a times depth z.

_{o}and θ

_{o}are the initial values of hydraulic conductivity and water content, respectively. For the determination of the fitting parameter γ$\left[\frac{1}{\mathsf{\gamma}}\right]$ and K

_{o}$\left[\frac{\mathrm{za}}{\mathsf{\gamma}}{\mathrm{e}}^{{\mathsf{\gamma}\mathrm{B}}_{\mathrm{L}}}\right]$, the linear semi log model expressed before (See Figure 2) was upgraded to:

#### 2.3. Root Mean Square Method

_{RMS}) was selected as an indicator of hydraulic properties variations of the soil using the data of water content from the IPM system during the infiltration phase. The D

_{RMS}is able to define the deviation distribution of the whole time series in one representative value [37]. The D

_{RMS}values cannot give an absolute rate of infiltration capacity reduction, but its factor of reduction can be used to infer it.

_{RMS}is calculated between the i-th infiltration cycle (i = 1,2, …, 9) and the first infiltration cycle in the time step t

_{x}like it is represented in Equation (7). This gives an approach of how much the averaged water content of each cycle changed in comparison to the initial state.

_{RMS}from Equation (7).

_{i}is the calculated infiltration capacity reduction in the i-th infiltration cycle (i = 1,2, …, 9) according to the tracer experiment; D

_{RMS i}is the calculated D

_{RMS}value (%) of the i-th infiltration cycle; and a, b and c are fitting parameters of the linear regression model. Once the model was determined the values from Equation (8) could be inserted and compared with the tracer curve data.

#### 2.4. Water Content Method

_{RMS}method, varying only in that instead of calculating the root mean square difference, the average water content of each infiltration cycle is calculated. Thus the infiltration time parameter of each infiltration cycle loses relevance. Similar to the previous method, a linear regression model was built and determined with the obtained data (Equation (9)).

_{i}is the calculated infiltration capacity reduction in the i-th infiltration cycle (i = 1,2, …, 9) according to the tracer experiment; $\frac{\sum {\mathrm{WC}}_{\mathrm{i}}}{{\mathrm{n}}_{\mathrm{i}}}$ is the averaged water content value (%) of the i-th infiltration cycle; n

_{i}is the amount of measured data in the i-th infiltration cycle; and a, b and c are fitting parameters of the linear regression model. This model was used afterwards to be compared to the tracer curve.

#### 2.5. Sensor Trigger Time Method

_{i}is the calculated infiltration capacity reduction in the i-th infiltration cycle (i = 1,2, …, 9) according to the tracer experiment; TT

_{i}is the trigger time (min) of the i-th infiltration cycle, where the water content started to rise and a, b and c are fitting parameters of the linear regression model. Just as with the other models, this model was analyzed by using the tracer curve.

## 3. Results and Discussion

#### 3.1. Tracer Method

_{50}of each infiltration cycle against the infiltration time is shown in Figure 3, which provides an indication of the infiltration rate reduction. Additionaly, the maximum infiltration rate reduction can be identified, which is important information for MAR plant managers for deciding when a maintenance action is required. The data obtained from the tracer test is used as a reference to analyze the fit of the alternative methods and their capacity to track changes of the hydraulic conductivity.

#### 3.2. Libardi Method

_{o}was set as the water content value when the drying process starts (a much slower process under gravitational forces) and θ is the water content in the time t

_{i}, which is represented in the abscissa of the smoothing model in Figure 2 as ln(t). Parameter A

_{L}and B

_{L}are represented as the slope and ordinate intercept, respectively (See Figure 2).

#### 3.3. Root Mean Square Method

_{RMS}values is similar with the one of the tracer curve. When applying the D

_{RMS}in the linear regression model (Equation (8)), the following equations for field and lab were obtained:

_{RMS}-based infiltration capacity reduction curve and the tracer-based curve fit well overall in the field experiment (Figure 6) with an RMSE of 0.14. In the lab experiment, the D

_{RMS}-based value gave an abrupt sink of the infiltration capacity after the third infiltration cycle, just similar as Libardi. Therefore the RMSE between the curves raised to 0.23.

#### 3.4. Water Content Method

_{RMS}and water content methods represent not only the wetting process at the beginning of the infiltration (for tracer method ~4 h), but also include the whole 24 h infiltration cycle behaviour. D

_{RMS}represents a more elaborate analysis in which data was also related in time. This may relate to the difference between both methods in the lab experiment. There was a lag phase of the water content in the infiltration cycles 4–6 that were interpreted by the D

_{RMS}method as a reduction of the infiltration capacity. The water content method sums up and averages also such differences, giving back more stable data.

#### 3.5. Sensor Trigger Time Method

## 4. Conclusions

_{RMS}and water content methods were the most accurately analyzed approaches for data management in MAR basins, to determine the actual state of the infiltration capacity and additionally they calculate a value that represents the complete infiltration cycle and not just a fraction of it.

_{RMS}, water content, and the trigger time methods all utilize linear regression models to correlates their raw data with the tracer experiments. The equations which are derived can only be used within each experiment, and in the analyzed intervals. If the boundary conditions remain the same in different experiments, the given empirical equation could also be applied.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Experimental set-up of infiltration laboratory scale unit (

**a**) and infiltration field scale unit (

**b**). Both units are filled with a sandy soil (Ks ≈ 6 × 10

^{−5}m/s) and are equiped with a sensor array measuring water content, matric potential, temperature, oxygen saturation and electrical conductivity [19].

**Figure 2.**Smoothed semi-log model designed by Hillel and Libardi [34] for the empirical determination of the hydraulic conductivity.

**Figure 3.**Infiltration rate curve determined by tracer experiments in (

**right**) field scale and (

**left**) lab scale. Infiltration modus: 24 h infiltration/72 h dry period.

**Figure 4.**Water content decrease during the drying cycles in the first 100 min in field experiment. Infiltration modus: 24 h infiltration/72 h dry period.

**Figure 5.**Infiltration capacity curve comparison between Libardi method and Tracer curve in (

**left**) field scale and (

**right**) lab scale. Infiltration modus: 24 h infiltration/72 h dry period.

**Figure 6.**Comparison between tracer curve and linear regression (LR) root mean square displacement (D

_{RMS})-based curve in (

**left**) field scale and (

**right**) lab scale.

**Figure 7.**Comparison between tracer curve and LR water content (WC)-based curve in (

**left**) field scale and (

**right**) lab scale.

**Figure 8.**Comparison between tracer curve and LR trigger time (TT)-based curve in (

**left**) field scale and (

**right**) lab scale.

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**MDPI and ACS Style**

Barquero, F.; Fichtner, T.; Stefan, C.
Methods of In Situ Assessment of Infiltration Rate Reduction in Groundwater Recharge Basins. *Water* **2019**, *11*, 784.
https://doi.org/10.3390/w11040784

**AMA Style**

Barquero F, Fichtner T, Stefan C.
Methods of In Situ Assessment of Infiltration Rate Reduction in Groundwater Recharge Basins. *Water*. 2019; 11(4):784.
https://doi.org/10.3390/w11040784

**Chicago/Turabian Style**

Barquero, Felix, Thomas Fichtner, and Catalin Stefan.
2019. "Methods of In Situ Assessment of Infiltration Rate Reduction in Groundwater Recharge Basins" *Water* 11, no. 4: 784.
https://doi.org/10.3390/w11040784