# A Comparative Study of Water and Bromide Transport in a Bare Loam Soil Using Lysimeters and Field Plots

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

## 1. Introduction

^{3}to 150 m

^{3}), (ii) their filling method (reconstituted or undisturbed soil), (iii) their lower limit (atmospheric pressure or controlled matric head), (iv) their instrumentation level, and (v) whether they are weighed or not [5,6,7]. Numerous studies have already been carried out on water content and solute transport with different types of lysimeters [8,9,10,11].

## 2. Materials and Methods

#### 2.1. Location, Climate, and Characteristics of the Soil

#### 2.2. Field plots

^{2}(9 × 10 m) bare soil field plots dating from 2000 have been instrumented since January 2013 with T4e tensiometers (UMS GmbH, Frankfurt am Main) and TDR CS605 probes (Campbell Scientific, Logan, UT) placed at eight depths: 10, 20, 37, 50, 65, 90, 120 and 165 cm. Calibration of the TDR probes was based on eleven gravimetric water content profiles measured between September 2013 and February 2015 (data not shown). Soil samples were taken from the same depths at the time of instrumentation for measuring (i) bulk density (ρ

_{b}) using cylinders of 50, 250 and 500 cm

^{3}[24], (ii) water retention (θ(h)) using cylinders of 50 cm

^{3}and the Richards press method [25], (iii) saturated hydraulic conductivity (${K}_{s}$) only for Field Plot 3 using cylinders of 250 cm

^{3}and the constant head method [26].

^{−}L

^{−1}The solution was pulverized using a 9 m ramp at a dose of 4 L m

^{−2}equivalent to 50 g Br

^{−}m

^{−2}. The transport of bromide ions was then studied based on four sample collection rounds (noted C

_{1}to C

_{4}), which were carried out 112, 279, 526 and 699 days after ploughing. Ploughing was performed on 22 February 2013 using a moldboard plough. Eleven profiles were measured in each round, separated by 0.5 to 1 m along a line perpendicular to the major axis of the plot. Each profile was sampled every 10 cm depth from 0 to 160 cm (0 to 120 cm for C

_{1}). Eight of the profiles were sampled using a motor-driven sample collector (MCL3, GEONOR Inc., Augusta, NJ—section 2.6 cm

^{2}) from 0 to 120 cm and then completed from 120 to 160 cm using an auger (section 3.8 cm

^{2}) enlarging the hole made by the corer. After C

_{2}, three additional profiles were sampled manually at every 10 cm from 0 to 160 cm, using a large-section auger (17.4 cm

^{2}). Bromide was extracted from the samples in the laboratory, using demineralized water, by shaking for one hour at 30 rpm. The bromide concentration was then measured in the supernatant by ionic chromatography using a Compact CI 882 Plus chain (Metrohm France SAS) according to the norm NF EN ISO 10304-1.

#### 2.3. Lysimeters

^{3}(2 × 2 × 1 m) black plastic containers with the bottom slightly inclined toward the center to facilitate water outflow and collection through a drainage hole placed in the middle. The bottom 10 cm consisted of coarse sand to facilitate drainage. When the lysimeters were put in place, the same soil granulometric, physical and chemical properties as those determined for the field plots were obtained. Many studies have been carried out on the six cultivated lysimeters since 1984 (e.g., leaching of nitrates and atrazine, preferential transport of pesticides) with different crop rotation between Lys. 1, 2 and 3 and Lys. 4, 5 and 6. The six lysimeters have been held in bare soil since 2008 and Lys. 1 was instrumented with TDR TRASE probes (Soil Moisture Equipment Corp., Santa Barbara, CA) in March 2009, and with T4e tensiometers in August 2011. Lys. 4 was equipped with TDR CS605 probes in August 2013. The instruments were inserted to the depths of 10, 20, 40, 60 and 80 cm. Tipping-counters (VKWA 100,UGT GmbH, Müncheberg) were installed in late March 2013 at the bottom of each lysimeter to ensure precise measurement of the water outflow over time.

^{−}m

^{−2}) using a movable, electric motor-powered, variable-speed irrigation ramp. Soil tillage was carried out immediately after application using a rotary drill to the depth of 10 cm. The transport of bromide ions was monitored over 127 samples taken from each lysimeter outflow over a period of almost two years (20 February 2013–5 February 2015). Bromide ion content in outflow samples was measured using ion chromatography as in the samples taken from the field plots.

#### 2.4. Climate Data

_{0}) was calculated based on these measurements using the Penman-Monteith equation [27]. Based on ET

_{0}, the maximum daily evaporation of bare soil (E

_{BS}) was estimated using a crop coefficient calculated monthly based on the FAO-56 method [28]. This potential evaporation value produces a satisfactory estimate for the daily value of E

_{BS}with a precision of ±15% according to the literature [29].

#### 2.5. Modelling

#### 2.5.1. Presentation of the Model

^{3}cm

^{−3}), t the time (d), z the coordinate along the vertical axis pointing negatively downwards (cm), h the soil matric head (cm) and K the hydraulic conductivity (cm d

^{−1}).

^{3}cm

^{−3}), α, an empirical parameter related to the matric head at the inflection point of the retention curve (cm

^{−1}) and n, a pore size distribution parameter (-) which determines the slope of the curve at the inflection point.

^{−1}), ${S}_{e}$, the effective saturation (-) and l, a pore connectivity parameter (-). The latter is most often kept constant regardless of soil type and fixed at 0.5 [33].

^{−3}), q, the water flux density (cm d

^{−1}) and D, the hydrodynamic dispersion coefficient (cm

^{2}d

^{−1}) [34] given by:

^{−1}), ${D}_{0}$, the solute molecular diffusion coefficient in pure water (1.584 cm

^{2}d

^{−1}for bromide) and τ, a tortuosity factor in liquid phase (-) [35] given by:

^{3}cm

^{−3}), ${\theta}_{im}$, the immobile water content (cm

^{3}cm

^{−3}), ${h}_{m}$, the matric head in the mobile region (cm) and ${h}_{im}$, the matric head in the immobile region (cm).

^{−1}).

#### 2.5.2. Representation of the Soil Profiles in HYDRUS-1D

#### 2.5.3. Initial and Boundary Conditions

_{BS}) and rainfall data.

_{0}was considered to be uniformly distributed over 0–10 cm.

^{−3}).

#### 2.5.4. Parameter Optimization Based on the Data Acquired from the Field Plots

- Initial values were obtained by using the Rosetta software [38] based on the particle size distribution measured for each soil material of each plot, its bulk density as well as its water content measured in the laboratory at −330 and −15,000 cm matric heads.
- These initial values were then used as input for the RetC software [39], which was used to fit the van Genuchten retention curve θ(h) to the measured water retention data. As recommended by Wösten and van Genuchten (1988) [40], the ${\theta}_{r}$ parameter was not optimized. The simulations based on these RetC parameters will be identified as RP165.
- The values and confidence intervals for parameters ${\theta}_{s}$, α and n calculated by the RetC software were then used as input in inverse simulations with HYDRUS-1D. Saturated hydraulic conductivity (${K}_{s}$) values obtained from laboratory measurements on Field Plot 3 were used to calculate initial values and confidence intervals for all field plots. The simulations based on these HYDRUS-1D inversed parameters will be identified as P165.

^{th}variable computed with the vector

**b**of parameters (${\theta}_{r}$, ${\theta}_{s}$, α, n, ${K}_{s}$), m the number of variables measured, ${n}_{j}$ the number of measurements for variable j, and finally ${v}_{j}$ and ${w}_{i,j}$ the weights associated with the measured variable j and with each individual value i of variable j. These weights were set to 1 since data are automatically rendered dimensionless by HYDRUS-1D.

#### 2.5.5. Parameter Optimization Based on the Data Acquired from the Lysimeters

#### 2.5.6. Cross Simulations

_{1p}to M

_{6p}) were consequently taken into account (Figure 1). The matric head data measured by the tensiometer located at 90 cm was used as the lower boundary condition. The simulation consisted in applying the mean values of the optimized parameters found for each soil material of all lysimeters to the corresponding soil materials of each field plot and comparing the result of the simulation to the water and bromide data obtained in the field plots (simulations noted L*). Similarly, the parameters estimated using field plot data were applied to simulate the lysimeter experiments (P* simulations).

#### 2.6. Evaluation of Simulation Quality

## 3. Results and Discussion

#### 3.1. Measurements

#### 3.1.1. Soil Physical Characteristics

#### 3.1.2. Water Dynamics

^{−1}compared to the other three lysimeters. This could be caused by the reconstitution of the lysimeters, as well as by different crop rotation conducted since their installation in 1983 and until 2007.

#### 3.1.3. Bromide Transport

_{1}(13 June 2013) and in Field Plot 3 at C

_{2}(27 November 2013), resulting in less accurate mass balances. The quantity of bromide leached out of the soil profile was negligible at C

_{1}and C

_{2}, whilst approximately 10 g m

^{−2}were leached on 1 August 2014 (C

_{3}), and even more at C

_{4}. The downward movement of bromide was the result of net infiltrations of 56 to 150 mm between each round of measurements, and mainly depended on daily rainfalls exceeding 10 mm. The number of these infiltrations varied between 8 and 13 and accounted for 40 to 56% of the total rainfall measured during each period.

^{−1}for a cumulative outflow of 196 to 241 mm. These water amounts are at least 16% lower than the water retention capacity measured in the lysimeters, which was estimated at 287 mm based on neutron probe measurements made in 2001. This would mean that some of the water contained in the lysimeters did not participate in the transport of bromide and that preferential flow [61,62] occurred. Several processes already reported in the literature could explain the preferential transport of bromide in the lysimeters, such as (i) the soil disturbance that may have induced differences in soil structure and porosity compared to the undisturbed soil of the field plots, at least for some time [63]; (ii) the modification of the soil water dynamics, induced by the rupture of capillarity at the bottom of the lysimeter [21]; (iii) the water content close to saturation [64] observed at 40 cm and deeper; (iv) the interruptions of drainage [12].

^{−2}, which represented between 69 and 89% of the application (50 g m

^{−2}).

#### 3.2. Modelling

#### 3.2.1. Field Plots

_{1p}to M

_{4p}) than those for horizons SCa and SCca (M

_{5p}to M

_{8p}) whilst the opposite was found for parameter n. However, these parameters did not allow to describe the water dynamics observed in situ in a satisfactory manner (RP165 in Figure 4 and Figure S7 and Table 3 and Table S4).

_{2p}, n for M

_{5p}and M

_{6p}and ${K}_{s}$ for M

_{3p}, Table 2 and Table S3) which is not the case for the soil materials within the same layer. This emphasizes the importance of defining as many soil materials as instrumented depths [37]. Confidence intervals associated with each optimized parameter are relatively small around the optimized value.

#### 3.2.2. Lysimeters

_{BS}) based on ET

_{0}could perhaps explain these differences. Only a few studies have been dedicated to the validation of the estimation of bare soil evaporation [71,72], in spite of the multitude of estimation methods [73]. In the absence of a means of comparison, the same daily values of E

_{BS}were considered for the field plots and for the lysimeters in spite of possible differences generally attributed to different water content profiles [74] and to the limited depth of the lysimeters [75].

_{2c}) turned out to be different from the other four soil materials (Table 7). Furthermore, given that the soil was continuously close to saturation at 40 cm depth and below, the problem of inversion occurring in lysimeters affected mostly the α, n and ${K}_{s}$ parameters, producing very large confidence intervals. Consequently, unlike for the field plots, many parameters (in italics in Table 7) could not be optimized and had to be calibrated manually. The few confidence intervals associated with optimized parameters were small around the optimized value. Finally, few optimized parameters on lysimeters are included in the confidence intervals of those of the field plots and vice versa (Table 2 and Table S3 vs. Table 7 and Table S8).

_{0}(C

_{0}* in Table 8 and Table S9), which is sometimes considerably different from the target quantity (50 g m

^{−2}). The results indicate a more uniform pulverization for Lys. 4, 5 and 6, which are closer to the target dose.

#### 3.2.3. Cross Simulations

^{3}cm

^{−3}and α

_{ph}= 10

^{−6}d

^{−1}). Indeed, simulated transport was too fast compared to observations whether the ${\theta}_{s}$ values were optimized again or not (L*_MIM and oL*_MIM in Figure 5 and Figure S8). This results in efficiency coefficients being lower than 0 when pooling all measurement campaigns conducted between June 2013 and August 2014 (L*_MIM and oL*_MIM in Table 4 and Table S5). Nevertheless, a better simulation of bromide transport was obtained when using the CDE model with parameters optimized on lysimeter data (L*_CDE and oL*_CDE in Figure 5 and Figure S8), except for the first sampling dates for Field Plots 2 and 3. In spite of this, the efficiency coefficients obtained were still lower than those calculated based on the parameters optimized on field plot data (L*_CDE and oL*_CDE vs. P90_CDE in Table 4 and Table S5). Consequently, the preferential transport observed in the lysimeters represents an artifact that does not allow an adequate simulation of the solute transport observed experimentally in the field plots, in spite of having their water dynamics adequately simulated once the ${\theta}_{s}$ values were optimized.

## 4. Summary and Conclusions

## Supplementary Materials

_{1}(a), C

_{2}(b), C

_{3}(c), and C

_{4}(d)), Figure S5: Bromide concentration (Lys. 2 and 5) and cumulative outflow (all lysimeters), as a function of cumulative drainage ((a); (c)) and time ((b); (d)), Figure S6. Comparison between experimental (obtained in the laboratory) and fitted (with RetC) water retention curves at the 10 (a), 20 (b), 37 (c), 50 (d), 65 (e), 90 (f), 120 (g) and 165 (h) cm depths on the three field plots, Figure S7. Comparison of experimental and simulated matric head and volumetric water content data at the 10 ((a); (b)), 37 ((c); (d)), 50 ((e); (f)) and 90 ((g); (h)) cm depths on Field Plots 2 and 3, Figure S8. Comparison between experimental and simulated bromide concentrations in Field Plots 2 and 3 for the four monitoring campaigns (C

_{1}(a), C

_{2}(b), C

_{3}(c), and C

_{4}(d)), Figure S9. Comparison between experimental and simulated volumetric water content data at the 10 (a), 20 (b), 40 (c), 60 (d) and 80 (e) cm depths on Lys. 4, Figure S10. Comparison between experimental and simulated bromide concentration and cumulative outflow as a function of cumulative drainage ((a); (c)) and time ((b); (d)) on Lys. 2, 3, 4, 5 and 6, Table S1. Particle size fractions (in %) of the eight soil materials of the three field plots, Table S2. Bulk density and saturated hydraulic conductivity mean values obtained at each instrumented depth in each field plot, Table S3. Parameters optimized using HYDRUS-1D for each of the eight soil materials of Field Plots 2 and 3, Table S4. Efficiency coefficients calculated at each instrumented depth in Field Plots 2 and 3 and based on different optimization procedures using HYDRUS-1D, Table S5. Efficiency coefficients calculated for bromide transport for each monitoring campaign (C

_{1}to C

_{4}) conducted on Field Plots 2 and 3 and based on different optimization procedures using HYDRUS-1D, Table S6. Efficiency coefficients calculated for water content data at each depth instrumented in Lys. 4 using HYDRUS-1D, Table S7. Efficiency coefficients calculated for daily drainage data on Lys. 2, 3, 4, 5 and 6 using HYDRUS-1D, Table S8. Parameters optimized using HYDRUS-1D for each of the six soil materials of Lys. 2, 3, 4, 5 and 6, Table S9. The values of dispersivity, immobile water content and mass exchange coefficient parameters manually set using HYDRUS-1D for all soil materials of Lys. 2, 3, 4, 5 and 6, Table S10. Efficiency coefficients calculated for bromide concentration and cumulated outflow as a function of time (and cumulative drainage in parentheses) from Lys. 2, 3, 4, 5 and 6 and based on different optimization procedures using HYDRUS-1D, Table S11. The mean values of the parameters optimized using HYDRUS-1D on the lysimeter data used for cross simulations on field plot data, Table S12. The mean values of the parameters optimized on the three field plots using HYDRUS-1D for cross simulations on lysimeter data.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Field plot (

**a**) and lysimeter (

**b**) soil profiles: horizons, discretization, observation nodes and soil materials considered in the HYDRUS-1D model.

**Figure 2.**Average profile of water content (

**a**) and hydraulic head (

**b**) observed from 22 February 2013 to 31 January 2015 in each instrumented field plot and lysimeter. Standard deviations are calculated from the daily data observed at each instrumented depth.

**Figure 3.**Comparison between experimental and simulated drainage on Lys. 1. L for results obtained with optimized parameters with HYDRUS-1D on lysimeter data; P* for results obtained by applying the mean optimized parameters from the 165 cm deep profile of the three field plots; oP*, the same as P* but for saturated water content values (${\theta}_{s}$*) again optimized for each soil material.

**Figure 4.**Comparison of experimental and simulated matric head and volumetric water content data at the 10 ((

**a**); (

**b**)), 37 ((

**c**); (

**d**)), 50 ((

**e**); (

**f**)) and 90 ((

**g**); (

**h**)) cm depths on Field Plot 1. RP165 for results obtained with the parameters optimized with RetC, P165 for results obtained with the parameters optimized with HYDRUS-1D on the 165 cm deep profile; P90 for results obtained by applying the parameters optimized for the 165 cm deep profile to the 90 cm deep profile; L* for results obtained by applying the mean optimized parameters from the six lysimeters; oL*, the same as L* but for saturated water content values (${\theta}_{s}$*) again optimized for each soil material.

**Figure 5.**Comparison between experimental and simulated bromide concentrations in Field Plot 1 for the four monitoring campaigns (C

_{1}(

**a**), C

_{2}(

**b**), C

_{3}(

**c**), and C

_{4}(

**d**)). Each experimental point is the average of 8 to 11 samples and is accompanied by its standard deviation. P165_CDE for results obtained with HYDRUS-1D with the convection-dispersion equation and parameters optimized on the 165 cm deep profile; L*_CDE for the results obtained with the convection-dispersion equation and by applying the mean optimized parameters from the six lysimeters; L*_MIM for the results obtained with the mobile-immobile model and by applying the mean optimized parameters from the six lysimeters; oL*, the same as L* but for saturated water content values (${\theta}_{s}$*) optimized again for each soil material. Results obtained with the convection-dispersion equation and parameters optimized on the 90 cm deep profile are not shown since no significant differences were found with P165_CDE for simulated bromide amount.

**Figure 6.**Comparison of experimental and simulated matric head and volumetric water content data at the 10 ((

**a**); (

**b**)), 20 ((

**c**); (

**d**)), 40 ((

**e**); (

**f**)) and 60 ((

**g**); (

**h**)) cm depths on Lys. 1. L for results obtained with the parameters optimized with HYDRUS-1D on lysimeter data; P* for results obtained by applying the mean optimized parameters from the 165 cm deep profile of the three field plots; oP*, the same as P* but for saturated water content values (${\theta}_{s}$, ${\theta}_{s}$*) again optimized for each soil material.

**Figure 7.**Comparison between experimental and simulated bromide concentration and cumulative outflow as a function of cumulative drainage ((

**a**); (

**c**)) and time ((

**b**); (

**d**)) on Lys. 1. L_CDE for results obtained with the convection-dispersion equation and parameters optimized with HYDRUS-1D on lysimeter data; L_MIM for results obtained with the mobile-immobile model and parameters optimized with HYDRUS-1D on lysimeter data; P*_CDE for results obtained with the convection-dispersion equation and by applying the mean optimized parameters from the 165 cm deep profiles of the three field plots; P*_MIM for the results obtained with the mobile-immobile model and by applying the mean optimized parameters from the 165 cm deep profiles of the three field plots. Results obtained with oP* are not shown since the bromide concentration dynamics found as a function of cumulative drainage and time were similar to P*.

**Table 1.**Particle size distribution and bulk density of the field plots and lysimeters. When available, standard deviations are reported in parentheses.

Layer (cm) | Field Plots (2012) | Lysimeters (1983) | ||||||
---|---|---|---|---|---|---|---|---|

Clay | Silt | Sand | ρ_{b} | Clay | Silt | Sand | ρ_{b} | |

(%) | (g cm^{−3}) | (%) | (g cm^{−3}) | |||||

0–30 | 23.6 (0.7) | 65.9 (0.8) | 10.5 (0.9) | 1.38 (0.11) | 23.9 | 69.2 | 6.9 | 1.34 |

30–60 | 23.7 (1.7) | 66.0 (0.9) | 10.3 (1.2) | 1.25 (0.07) | 23.3 | 70.4 | 6.4 | 1.22 |

60–90 | 16.4 (1.7) | 68.6 (1.5) | 15.0 (1.3) | 1.41 (0.08) | 17.5 | 72.3 | 10.3 | 1.37 |

Soil Material | ${\mathit{\theta}}_{\mathit{r}}$ | ${\mathit{\theta}}_{\mathit{s}}$ | α | n | ${\mathit{K}}_{\mathit{s}}$ | λ | ${\mathit{\theta}}_{\mathit{s}}\ast $ |
---|---|---|---|---|---|---|---|

cm^{3} cm^{−3} | cm^{−1} | - | cm d^{−1} | cm | cm^{3} cm^{−3} | ||

M_{1p} | 0.066 (0.073) [0.066–0.076] | 0.364 (0.411) [0.359–0.368] | 0.021 (0.054) [0.020–0.023] | 1.252 (1.162) [1.240–1.264] | 101.2 | 4.0 | 0.329 [0.327–0.330] |

M_{2p} | 0.076 (0.077) [0.076–0.079] | 0.381 (0.439) [0.370–0.391] | 0.077 (0.196) [0.067–0.087] | 1.144 (1.139) [1.133–1.155] | 776.8 [571.4–982.2] | 4.0 | 0.317 [0.316–0.319] |

M_{3p} | 0.075 (0.076) [0.075–0.080] | 0.373 (0.420) [0.370–0.376] | 0.036 (0.028) [0.034–0.038] | 1.181 (1.162) [1.161–1.200] | 45.6 | 4.0 | 0.325 [0.323–0.327] |

M_{4p} | 0.065 (0.068) [0.065–0.070] | 0.313 (0.448) [0.295–0.330] | 0.007 (0.076) [0.001–0.012] | 1.364 (1.183) [1.343–1.384] | 76.9 | 4.0 | 0.299 [0.297–0.301] |

M_{5p} | 0.046 (0.048) [0.046–0.051] | 0.320 (0.412) [0.306–0.335] | 0.017 (0.043) [0.012–0.021] | 1.158 (1.204) [1.116–1.200] | 27.1 [7.9–46.3] | 1.5 | 0.302 [0.300–0.304] |

M_{6p} | 0.050 (0.051) [0.050–0.055] | 0.327 (0.395) [0.322–0.332] | 0.004 (0.007) [0.002–0.006] | 1.654 (1.279) [1.442–1.867] | 16.7 | 1.5 | 0.315 [0.313–0.317] |

M_{7p} | 0.041 (0.044) [0.041–0.047] | 0.351 (0.394) [0.342–0.360] | 0.002 (0.005) [0.002–0.002] | 1.452 (1.452) | 16.1 | 3.0 | / |

M_{8p} | 0.040 (0.037) [0.036–0.040] | 0.390 (0.311) [0.382–0.398] | 0.006 (0.002) [0.006–0.006] | 1.463 (1.463) | 19.8 | 3.0 | / |

**Table 3.**Efficiency coefficients calculated at each instrumented depth in Field Plot 1 and based on different optimization procedures using HYDRUS-1D. RP165 for results obtained with the parameters optimized with RetC, P165 for results obtained with the parameters optimized with HYDRUS-1D on the 165 cm deep profile; P90 for results obtained by applying the parameters optimized for the 165 cm deep profile to the 90 cm deep profile; L* for results obtained by applying the mean optimized parameters from the six lysimeters; oL*, the same as L* but for saturated water content values (${\theta}_{s}$*) again optimized for each soil material.

Simulation | M_{1p}_10 | M_{2p}_20 | M_{3p}_37 | M_{4p}_50 | M_{5p}_65 | M_{6p}_90 | M_{7p}_120 | M_{8p}_165 |
---|---|---|---|---|---|---|---|---|

h_RP165 | 0.21 | 0.06 | −0.71 | −1.26 | −0.81 | 0.86 | 0.86 | 1.00 |

h_P165 | 0.48 | 0.47 | 0.72 | 0.78 | 0.79 | 0.88 | 0.87 | 1.00 |

h_P90 | 0.49 | 0.46 | 0.69 | 0.83 | 0.78 | 1.00 | / | / |

h_L* | 0.41 | 0.43 | 0.48 | 0.63 | 0.76 | 1.00 | / | / |

h_oL* | 0.48 | 0.44 | 0.51 | 0.66 | 0.76 | 1.00 | / | / |

θ_RP165 | −1.39 | −1.76 | −9.92 | −17.73 | −22.48 | −35.59 | −13.52 | −19.88 |

θ_P165 | 0.65 | 0.58 | 0.64 | 0.71 | 0.84 | 0.73 | 0.67 | 0.83 |

θ_P90 | 0.67 | 0.61 | 0.71 | 0.81 | 0.80 | 0.44 | / | / |

θ_L* | 0.21 | −0.31 | −0.76 | −7.35 | −133.53 | −69.30 | / | / |

θ_oL* | 0.62 | 0.30 | 0.38 | 0.39 | 0.84 | 0.80 | / | / |

**Table 4.**Efficiency coefficients calculated for bromide transport for each monitoring campaign (C

_{1}to C

_{4}) conducted on Field Plot 1 and based on different optimization procedures using HYDRUS-1D.

Simulation | C_{1} (13 June 2013) | C_{2} (27 November 2013) | C_{3} (1 August 2014) | C_{4} (21 January 2015) |
---|---|---|---|---|

P165_CDE | 0.93 | 0.80 | 0.93 | 0.89 |

P90_CDE | 0.87 | 0.82 | 0.80 | / |

L*_CDE | 0.74 | 0.84 | 0.20 | / |

oL*_CDE | 0.84 | 0.65 | −0.73 | / |

L*_MIM | 0.30 | 0.11 | −1.37 | / |

oL*_MIM | 0.38 | −0.47 | −1.57 | / |

**Table 5.**Efficiency coefficients calculated for matric head and water content data at each depth instrumented in Lys. 1 using HYDRUS-1D.

Simulation | M_{1c}_10 | M_{2c}_20 | M_{3c}_40 | M_{4c}_60 | M_{5c}_80 |
---|---|---|---|---|---|

h_L | 0.74 | 0.54 | −0.14 | −0.93 | −0.07 |

h_P* | −0.06 | 0.17 | −0.72 | −1.59 | 0.53 |

h_oP* | −0.06 | 0.17 | −0.80 | −1.60 | 0.54 |

θ_L | 0.62 | 0.41 | 0.43 | 0.07 | 0.05 |

θ_P* | −5.69 | −1.59 | −9.97 | −142.89 | −165.11 |

θ_oP* | 0.33 | 0.36 | 0.36 | 0.37 | 0.43 |

Simulation | Lys. 1 |
---|---|

d_L | 0.81 |

CV | −1.2 |

d_P* | 0.79 |

CV | −14.7 |

d_oP* | 0.79 |

CV | −14.9 |

Soil Material | ${\mathit{\theta}}_{\mathit{r}}$ | ${\mathit{\theta}}_{\mathit{s}}$ | α | n | ${\mathit{K}}_{\mathit{s}}$ | ${\mathit{\theta}}_{\mathit{s}}\ast $ |
---|---|---|---|---|---|---|

cm^{3} cm^{−3} | cm^{−1} | - | cm d^{−1} | cm^{3} cm^{−3} | ||

M_{1c} | 0.062 (0.072) [0.062–0.108] | 0.289 (0.402) [0.287–0.291] | 0.020 (0.047) [0.020–0.020] | 1.194 (1.168) [1.189–1.200] | 10.0 (110.2) | 0.286 [0.282–0.290] |

M_{2c} | 0.097 (0.078) [0.069–0.097] | 0.288 (0.394) [0.286–0.290] | 0.200 (0.084) | 1.050 (1.168) | 1000.0 (575.2) | 0.324 [0.320–0.329] |

M_{3c} | 0.109 (0.080) [0.065–0.109] | 0.366 (0.423) [0.364–0.368] | 0.035 (0.055) | 1.100 (1.174) | 30.0 (73.9) | 0.384 [0.380–0.388] |

M_{4c} | 0.065 (0.075) [0.065–0.095] | 0.389 (0.431) [0.387–0.391] | 0.012 (0.068) | 1.140 (1.181) | 15.0 (76.9) | 0.410 |

M_{5c} | 0.058 (0.049) [0.043–0.058] | 0.396 (0.394) [0.394–0.398] | 0.009 (0.021) | 1.150 (1.252) | 25.0 (22.9) | 0.397 |

M_{6c} | 0.010 | 0.450 | 0.150 | 3.000 | 3000.0 | / |

**Table 8.**Values of dispersivity, immobile water content and mass exchange coefficient parameters manually set using HYDRUS-1D for all soil materials of Lys. 1. Initial amounts of bromide manually re-optimized are noted C

_{0}*.

Parameter | Lys. 1 |
---|---|

λ [cm] | 2.00 |

${\theta}_{im}$[cm^{3} cm^{−3}] | 0.060 |

C_{0}* [g m^{−2}] | 59.2 |

${\alpha}_{ph}$[d^{−1}] | 10^{−6} |

**Table 9.**Efficiency coefficients calculated for bromide concentration and cumulated outflow as a function of time (and cumulative drainage in parentheses) from Lys. 1 and based on different optimization procedures using HYDRUS-1D.

Variable | Simulation | Lys. 1 |
---|---|---|

Concentration | L_CDE | 0.37 (0.61) |

L_MIM | 0.83 (0.93) | |

P*_CDE | 0.34 (0.80) | |

P*_MIM | 0.84 (0.67) | |

Cumulated Outflow | L_CDE | 0.08 (0.32) |

L_MIM | 0.60 (0.63) | |

P*_CDE | 0.41 (0.39) | |

P*_MIM | 0.90 (0.18) |

© 2019 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/).

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**MDPI and ACS Style**

Isch, A.; Montenach, D.; Hammel, F.; Ackerer, P.; Coquet, Y.
A Comparative Study of Water and Bromide Transport in a Bare Loam Soil Using Lysimeters and Field Plots. *Water* **2019**, *11*, 1199.
https://doi.org/10.3390/w11061199

**AMA Style**

Isch A, Montenach D, Hammel F, Ackerer P, Coquet Y.
A Comparative Study of Water and Bromide Transport in a Bare Loam Soil Using Lysimeters and Field Plots. *Water*. 2019; 11(6):1199.
https://doi.org/10.3390/w11061199

**Chicago/Turabian Style**

Isch, Arnaud, Denis Montenach, Frederic Hammel, Philippe Ackerer, and Yves Coquet.
2019. "A Comparative Study of Water and Bromide Transport in a Bare Loam Soil Using Lysimeters and Field Plots" *Water* 11, no. 6: 1199.
https://doi.org/10.3390/w11061199