# Spatial and Seasonal Variations of Water and Salt Movement in the Vadose Zone at Salt-Impacted Sites

^{*}

## Abstract

**:**

## 1. Introduction

^{9}ha in the world [8].

## 2. Theoretical Considerations

#### 2.1. Water Flow and Solute Transport in Variably Saturated Soils

^{3}/L

^{3}), t is time (T), h is the soil water pressure head (L), z is the vertical spatial coordinate (L), K(h) is the unsaturated hydraulic conductivity function (L/T) and S is the sink term (L

^{3}/L

^{3}T) that accounts, for example, for root water uptake (transpiration).

_{s}is the saturated water content (L

^{3}/L

^{3}), θ

_{r}is the residual water content (L

^{3}/L

^{3}), α (1/L), n (−), and m (−) are curve fitting parameters, and other parameters are as defined earlier. The parameter α can be related to the inverse of air entry value (also referred to as the bubbling pressure which is the negative pressure head that must be exceeded before air recedes into the soil pores [21]. The parameter n is related to the pore size distribution index. Using the assumption that m = 1 − 1/n, van Genuchten [19] formulated the following equation for the unsaturated hydraulic conductivity function:

_{e}, is computed as shown below:

_{s}is the saturated hydraulic conductivity (L/T); $\ell $ (−) is an empirical parameter that is normally assumed to be 0.5 [15] and all the other parameters are as described earlier. It should be noted that in most instances, Equation (2) is fitted to the measured SWCC data and the fitted parameters are used to estimate the unsaturated hydraulic conductivity function using Equation (3).

^{−3}), q is the volumetric flux density (LT

^{−1}), and D

_{e}is the hydrodynamic dispersion coefficient (L

^{2}T

^{−1}).

_{w}is the moLecular diffusion coefficient in free water (L

^{2}T

^{−1}), τ

_{w}is a tortuosity factor in the liquid phase (−), |q| is the absolute value of the Darcian fluid flux density (LT

^{−1}), and D

_{L}is the longitudinal dispersivity (L).

#### 2.2. Soil Atmosphere Interactions

^{−1}) is the maximum rate of I or E across the soil atmosphere interface and h

_{A}and h

_{S}are the minimum and maximum pressure heads, respectively, allowed under the prevailing soil conditions. The value of h

_{A}can be calculated from the air humidity, H

_{r}, as follows [15]:

_{r}is relative humidity of the atmosphere (dimensionless); R is the gas constant (8.31 kg m

^{2}s

^{−2}K

^{−1}g moL

^{−1}); M is the moLecular weight of water (0.018 kg g moL

^{−1}); g is the gravitational acceleration (9.81 m s

^{−2}); and T is the temperature (K). In instances where the precipitation (P) rate exceeds the I capacity of the soil, the BC at the soil surface is changed from prescribed flux (precipitation flux) to head boundary (h = h

_{s}) and any excess water on the soil surface is immediately removed as a surface runoff (RO). Similarly, in instances that the potential evaporation (PE) rate exceeds the capability of the soil to deliver enough water toward the soil surface (h ≤ h

_{A}) the system-dependent BC changes from prescribed flux (PE rate), to head boundary. In this case, the PE reduces actual evaporation (AE) that is estimated by the prevailing pressure head at the ground surface.

## 3. Materials and Methods

#### 3.1. Meteorological Data Input

_{m}is the 1955 Thornthwaite’s annual moisture index, P

_{a}is the total annual precipitation (compiled from weather stations), and PE

_{a}is the annual PE. PE was estimated using the Penman method [28] and the compiled climate data. The moisture index may vary from positive values indicating moist/humid climates to negative values indicating dry climates. An I

_{m}value of zero signifies that the annual precipitation and PE are equal. Based on the computed annual moisture indices, the climate classification for various locations in the province of Alberta (Figure 2) can be divided into three main climate conditions as follows: dry sub-humid (Bighorn Dam and Edson); semi-arid (high level, Fort McMurray, Beaverlodge, high prairie, Lloydminster, Neir AEDM); and arid (Calgary and Medicine Hat).

#### 3.2. Soil Hydraulic Properties

#### 3.3. Model Development

## 4. Results and Discussion

#### 4.1. Arid Climatic Condition

#### 4.2. Semi-Arid Climatic Condition

_{s}of the coarse-grained material and only 0.6 mm/h higher than the K

_{s}of the fine-grained material. However, there was only one precipitation event greater than 2.0 mm/h during the period of analysis. Therefore, the RO was expected to be negligible.

_{semi-arid}/NI

_{arid}= 1.25). This observation leads one to conclude that the downward movement in coarse-grained materials for semi-arid climatic conditions could potentially be higher than that in arid climatic conditions.

#### 4.3. Dry Sub-Humid Climatic Condition

_{s}of the coarse-grained material (K

_{s}= 297 mm/h) and only 0.9 mm/h higher than the K

_{s}of the fine-grained material (K

_{s}= 2.0 mm/h). However, this event was recorded to occur only once over the 9-year period considered in this study.

_{dry-subhumid}/NI

_{semi-arid}= 1.32) and arid climatic conditions (NI

_{dry-subhumid}/NI

_{arid}= 1.66). This observation leads one to conclude that the downward solute displacement would be faster than the semi-arid climatic conditions and much faster than that in arid climatic conditions.

#### 4.4. Detailed Water Balance Assessment

## 5. Concluding Remarks

_{m}(Thornthwaite and Hare, 1955) [27]. An I

_{m}value of zero signifies that the annual precipitation and PE are equal. The compiled data revealed that for the province of Alberta, annual PE values are higher than the annual precipitation values. As such, in general, moisture loss conditions can be expected across the province. However, it should be noted that the I

_{m}and many other indices such as Thornwaite moisture index (TMI, as cited by Thornwaite, C.W., 1948) [26] are estimated based on the assumption that limitless supply of water is available to meet the evaporative demand dictated by prevailing atmospheric conditions. This assumption is only valid for water bodies or soil surfaces, which always remain saturated. The AE is not only the function of prevailing atmospheric conditions but also the transient soil moisture conditions. This is essentially the crux of this research as it was shown that transient soil moisture conditions are a function of soil texture and play a crucial role not only in subsurface flow and transport but also in the water balance at the ground surface. The accurate estimation of the AE requires a multiyear accurate climate dataset. Therefore, it can be concluded that the site-specific climate data are essential for accurate estimation of water balance at a particular site.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 4.**Soil–water characteristic curves for various soils from the United States Department of Agriculture (USDA) textural triangle.

**Figure 5.**Estimated water balance for different climatic conditions: (

**a**) arid, (

**b**) semi-arid, and (

**c**) dry sub-humid.

**Figure 6.**Vertical solute displacement over time in different climatic conditions; (

**a**) arid, (

**b**) semi-arid, and (

**c**) dry sub-humid.

**Figure 7.**Measured precipitation intensities over the nine-year period for three different climatic conditions in Alberta.

**Figure 8.**Daily precipitation occurrence over the nine-year period for three different climatic conditions in Alberta.

**Figure 9.**Calculated daily potential evaporation box–whisker plots for three different climatic conditions in Alberta.

**Figure 10.**Estimated water balance in the soil domain for three different climate conditions coarse-grained (

**a**) and fine-grained (

**b**) soil materials.

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**MDPI and ACS Style**

Bashir, R.; Pastora Chevez, E.
Spatial and Seasonal Variations of Water and Salt Movement in the Vadose Zone at Salt-Impacted Sites. *Water* **2018**, *10*, 1833.
https://doi.org/10.3390/w10121833

**AMA Style**

Bashir R, Pastora Chevez E.
Spatial and Seasonal Variations of Water and Salt Movement in the Vadose Zone at Salt-Impacted Sites. *Water*. 2018; 10(12):1833.
https://doi.org/10.3390/w10121833

**Chicago/Turabian Style**

Bashir, Rashid, and Eric Pastora Chevez.
2018. "Spatial and Seasonal Variations of Water and Salt Movement in the Vadose Zone at Salt-Impacted Sites" *Water* 10, no. 12: 1833.
https://doi.org/10.3390/w10121833