# Experimental Measurement of Diffusive Extinction Depth and Soil Moisture Gradients in a Dune Sand Aquifer in Western Saudi Arabia: Assessment of Evaporation Loss for Design of an MAR System

^{1}

^{2}

^{3}

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## Abstract

**:**

## 1. Introduction

## 2. Background and Methods

#### 2.1. Collection of Sand Samples from Dune Fields

#### 2.2. Grain Size Distribution Analyses

#### 2.3. Laboratory Porosity and Hydraulic Conductivity Measurements

#### 2.4. Calibration of Moisture Sensors

_{w}(m

^{3}/m

^{3}) = 4.3 × 10

^{−6}ε

_{r}

^{3}− 5.5 × 10

^{−4}ε

_{r}

^{2}+ 2.92 × 10

^{−2}ε

_{r}− 5.3 × 10

^{−2}

_{w}is soil moisture content and ε

_{r}is permittivity of soil. The natural variation in the characteristics of most soils causes the generic calibration for ECH2O soil moisture sensors to have an error of approximately ± 3%–4%. The error can be reduced to ± 1%–2% for all soils by using a soil specific calibration. Thus, the sensors were calibrated to obtain the best possible accuracy in volumetric water content measurements before using them in the experiment.

_{w}) of the sand for each sample using Equation (2) for each sample; (10) after calculating the:

_{r})) on the x-axis and the water content (moisture, (permittivity (ε

_{r})) on the y-axis, and (11) regression analysis was applied to a find best-fitting cubic polynomial between the parameters resulting in the best-fit curve shown in Figure 2.

**Figure 2.**Plot showing the relationship between permittivity (ε

_{r}) and soil moisture content (θ

_{w}).

#### 2.5. Experimental Design and Instrumentation

**Figure 3.**Schematic diagram of the setup to monitor water level, temperature and soil moisture gradients.

^{3}water was injected in the barrel. Soil moisture content and temperature were recorded throughout the filling process. Upon being satisfied that the sand was fully saturated with no significant trapped air in the barrel, the system was left to record evaporation loss from the sand.

#### 2.6. Hydrodynamic Modeling

_{v}+ θ

_{l}) of the volumetric water vapor content, θ

_{v}, and the volumetric liquid water content, θ

_{l}(both expressed as an equivalent water content), θ(h) is the water content as a function of pressure head (cm

^{3}·cm

^{−3}), T is temperature (K), K

_{lh}is isothermal hydraulic conductivity for the liquid phase (cm·s

^{−1}), K

_{LT}is thermal hydraulic conductivity for the liquid phase (cm·K

^{−1}·s

^{−1}), K

_{vh}is isothermal vapor hydraulic conductivity (cm·s

^{−1}), z is the depth positive downward in cm, and S is a sink term usually used to account for root water uptake (s

^{−1}).

_{r}and θ

_{s}are the residual and saturated water contents (cm

^{3}·cm

^{−3}), respectively, α (cm

^{−1}) and n (–) are shape parameters which are inversely related to the air entry value and the width of the pore size distribution, respectively, and m is defined as m = 1−1/n with n > 1 [28]. The isothermal unsaturated hydraulic conductivity is given by:

_{s}is the saturated hydraulic conductivity (cm·h

^{−1}), λ (−) represents pore tortuosity, and r determines the shape of the hydraulic conductivity function. θ

_{r}is the residual water content. It is used as an empirical parameter which is either given the value of zero or the value which best fits the water retention data or it can be derived from soil texture using the pedo-transfer function. θ

_{s}can be obtained by fully saturating the sand sample and then drying the sample in an oven for 24 h at 110 °C. The value of λ generally used is 0.5 or it can be estimated from bulk density and hydraulic conductivity with which it is highly correlated [35]. Values of α and n were obtained from the Rosetta database and are 0.145 and 2.18, respectively [Rosetta].

_{LT}, in Equation (3) is defined as follows [36]:

_{wT}is the grain factor (unitless), which quantifies the temperature dependence of the soil water retention curve [37], $\mathsf{\gamma}$ is the surface tension of soil water (J·m

^{−2}), and ${\mathsf{\gamma}}_{0}$ is the surface tension at 25 °C (= 71.89 g·s

^{−2}). The temperature dependence of $\mathsf{\gamma}$ is given by:

^{−2}and T in °C. The isothermal, K

_{vh}and thermal, K

_{vT}, vapor hydraulic conductivities are described by Nassar and Horton [38].

## 3. Results

#### 3.1. Physical Properties of the Media

Parameter | Sample 1 | Sample 2 | Sample 3 | Sample 4 | Sample 5 |
---|---|---|---|---|---|

Porosity | 0.41 | - | 0.33 | - | 0.40 |

Hydraulic Conductivity (m/day) | 6.48 | 3.30 (?) | 6.75 | 7.57 | 7.54 |

#### 3.2. Water Level Profile

#### 3.3. Soil Moisture Content Profile

**Figure 6.**Soil moisture content variations recorded by sensors (

**a**) from 3 to 7 cm of depth; (

**b**) 12 to 35 cm of depth; and (

**c**) from 40 to 100 cm of depth.

#### 3.4. Temperature Profile

**Figure 7.**Temperature fluctuations recorded by the sensors (

**a**) from depths of 3–7 cm; (

**b**) from depths of 12–35 cm; and (

**c**) from depths of 40–100 cm.

#### 3.5. Hydrodynamic Modeling Results

_{p}” was estimated using the FAO-56 method as described by Allen et al. [40] (Figure 9). The method used first calculated the potential evaporation from a grass ground-cover reference E

_{r}using the modified Penman-Monteith equation [40]. Hourly average values of various meteorological variables, including air temperature, relative humidity, wind speed, incoming shortwave radiation, and barometric pressure, were input into the model. Then, the reference evapotranspiration is scaled with an empirical coefficient which is E

_{p}= 1.15E

_{r}[34]. This coefficient defines the higher rate of diffusive evaporation potential of bare soil as compared to the reference grass cover [41].

^{3}·cm

^{−3}) obtained from the laboratory experiment. The sand in the top 7 cm was not completely saturated because water was added from the perforated pipes from the bottom upwards (to avoid air entrapment). Furthermore, the water added from the bottom via the perforated pipes needed more time to get imbibed in the sand to have a stable level near the surface.

#### 3.6. Comparison of Sensor and MVG Model Results

**Figure 12.**Soil water content θw measured by sensors versus soil water content obtained by hydrodynamic modeling at shallow (

**a**) and greater (

**b**) depths. Blue line represents 1:1 line and red is the best linear fit.

^{2}value of 0.84 and 0.71, for shallow and greater depths, respectively. Comparing model results with the measured data shows a model overestimation at depths of 25–45 cm and an underestimation from 5 to 12 cm. Detailed comparisons of the sensor and model estimations are shown in Figure 12a,b.

## 4. Discussion

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Mughal, I.; Jadoon, K.Z.; Mai, P.M.; Al-Mashharawi, S.; Missimer, T.M.
Experimental Measurement of Diffusive Extinction Depth and Soil Moisture Gradients in a Dune Sand Aquifer in Western Saudi Arabia: Assessment of Evaporation Loss for Design of an MAR System. *Water* **2015**, *7*, 6967-6982.
https://doi.org/10.3390/w7126669

**AMA Style**

Mughal I, Jadoon KZ, Mai PM, Al-Mashharawi S, Missimer TM.
Experimental Measurement of Diffusive Extinction Depth and Soil Moisture Gradients in a Dune Sand Aquifer in Western Saudi Arabia: Assessment of Evaporation Loss for Design of an MAR System. *Water*. 2015; 7(12):6967-6982.
https://doi.org/10.3390/w7126669

**Chicago/Turabian Style**

Mughal, Iqra, Khan Z. Jadoon, P. Martin Mai, Samir Al-Mashharawi, and Thomas M. Missimer.
2015. "Experimental Measurement of Diffusive Extinction Depth and Soil Moisture Gradients in a Dune Sand Aquifer in Western Saudi Arabia: Assessment of Evaporation Loss for Design of an MAR System" *Water* 7, no. 12: 6967-6982.
https://doi.org/10.3390/w7126669