Soil Science Soil Water Flow: Saturated, Unsaturated, and Preferential

Previous Lecture Review

  • Water Potential Measurement: Discussed methods like pressure plates, pressure membranes, and tension tables. Tension tables are only useful for very low tension, suitable for the wettest end of soil conditions.

Types of Water Flow in Soil

  • Saturated Flow:

    • Occurs when soil pores are completely full of water (i.e., at 100\% saturation, or
      \theta_s).

    • Water moves through continuously connected water-filled pores.

    • Typically observed right after heavy rain or irrigation, or when the soil surface is below the water table.

  • Unsaturated Flow:

    • Occurs when pores are partially full, meaning both air and water are present in the pores.

    • Water passes through these partially filled pores.

    • Defined when matric potential is less than 0 (\Psi < 0) and greater than -3100 kilopascals.

    • Overall flow is slower due to less water connectivity.

  • Vapor Flow:

    • Occurs in very dry conditions where water primarily moves as vapor.

    • This happens at the more dry end of the soil moisture spectrum.

Saturated Flow: Factors Affecting Water Movement

  • Pore Size: Larger pores (macropores) offer less friction between water and solid surfaces, leading to faster flow.

  • Soil Texture:

    • Coarse Texture (e.g., Sandy Soil): Characterized by larger macropores, resulting in faster saturated flow.

    • Fine Texture (e.g., Clay Soil): Generally has smaller pores.

  • Aggregation: Stable aggregates create large pore spaces between them, facilitating faster flow.

  • Pore Connectivity (Tortuosity):

    • Soil pores are not straight capillaries; they are tortuous and have various pathways.

    • If a pathway is disconnected, water must find an alternative route, slowing overall movement.

    • Tortuosity describes the actual path length water travels divided by the straight-line distance. Higher tortuosity leads to slower flow for a given cross-section.

  • Impact of Clay Type (Example: Vertisols vs. Ultisols):

    • Vertisols: Contain expandable clays (e.g., smectite). When wet, these clays expand, causing pore spaces to become smaller and reducing macropores. This limits water flow and drainage.

    • Ultisols: Often contain non-expanding clays (e.g., kaolinite) and iron/aluminum oxide coatings, leading to more stable aggregates. They experience no major change in pore size when wet, allowing for faster flow and drainage.

  • Oxisols: Despite potentially high clay content, their strong aggregation (due to metal oxides like aluminum and iron) causes particles to behave like sand. This allows many Oxisols to drain very well.

  • Water Films: In soil, water forms films around particles. These films are held tightly. In coarse soils, there are larger pores and less overlap of water films, allowing faster movement compared to fine soils.

Darcy's Law for Saturated Flow

  • Henry Darcy: A French engineer known for formulating Darcy's Law.

  • Purpose: Expresses the relationship between volumetric water flux, saturated hydraulic conductivity, and the hydraulic gradient.

  • Equation:

    • q = -K_{sat} \frac{\Delta\Psi}{\Delta L} where:

      • q = Volumetric water flux (e.g.,
        \frac{m^3}{m^2 \cdot s} or
        \frac{m}{s} if considering the cross-sectional area as the reference).

      • K_{sat} = Saturated hydraulic conductivity (e.g.,
        \frac{m}{s} or
        \frac{cm}{s}).

      • \frac{\Delta\Psi}{\Delta L} = Hydraulic gradient, which is the ratio of the change in water potential (\Delta\Psi) over the length (\Delta L) the water moves. Water potential can be expressed in units of height (e.g., cm).

  • Analogy: Similar to Ohm's Law (electrical resistivity) and Fourier's Law (heat expansion).

  • Example Calculation 1:

    • Setup: A soil column (length 40 \text{ cm}) with a constant water reservoir above (water level 10 \text{ cm} above soil surface). Water flows freely out the bottom.

    • Reference Point: Bottom of the soil column.

    • Gravimetric Potential at Reference: 0

    • Hydrostatic Potential at Reference:
      0

    • Total Water Potential at top of water column (above soil): 10 \text{ cm (static head) } + 40 \text{ cm (gravimetric)} = 50 \text{ cm}

    • Hydraulic Gradient:
      \frac{50 \text{ cm}}{40 \text{ cm}} = 1.25

    • If flux q = 0.015 \text{ cm/s}, then rearranging Darcy's Law: \ K_{sat} = \frac{q}{(\frac{\Delta\Psi}{\Delta L})} = \frac{0.015 \text{ cm/s}}{1.25} = 0.012 \text{ cm/s} (assuming the sign convention is handled).

  • Example Calculation 2 (Changed Outlet):

    • Setup: Same soil column, but the outlet pipe is raised so water exits at the level of the soil surface (effectively, the static head is now 0 at the top of the soil).

    • K_{sat}: Remains the same (0.012 \text{ cm/s}) as it's a soil property.

    • Water Potential at top of water column (at soil surface): 10 \text{ cm (hydrostatic head)} + 0 \text{ cm (gravimetric if ref is top of soil)} = 10 \text{ cm}

    • Hydraulic Gradient:
      \frac{10 \text{ cm}}{40 \text{ cm}} = 0.25

    • New Flux (q): \ q = K_{sat} \cdot \frac{\Delta\Psi}{\Delta L} = 0.012 \text{ cm/s} \cdot 0.25 = 0.003 \text{ cm/s} (approximately 28\% of students got this right).

  • Units: We can use pressure units (e.g., pascals) or height units (e.g., cm) for water potential, but consistency is key. Using height units simplifies calculations.

  • Typical K_{sat} Values:

    • Sandy Soil: Higher K_{sat}.

    • Clay Soil: Much lower K_{sat}.

    • Vertisols/Landfills: Can have very low K_{sat} (e.g., 10^{-7} to 10^{-9} \text{ cm/s}) if lined with clays to prevent seepage.

Preferential Flow in Saturated Conditions

  • Heterogeneous Matrix: Landscape soils are heterogeneous; water doesn't always move uniformly.

  • Cracks (e.g., Vertisols): Large cracks in vertisols act as conduits, allowing water to move much faster than predicted by Darcy's Law for the bulk soil matrix. This can lead to faster field drainage and contaminant transport (e.g., phosphorus fertilization study in Israel).

Unsaturated Flow: Detailed Analysis

  • Conditions: Occurs when matric potential (\Psi) is between 0 and -3100 kPa.

  • Mechanism: Less water connectivity necessitates water taking longer, more tortuous routes to maintain connection, thus decreasing flow rates.

  • Unsaturated Hydraulic Conductivity (K(\Psi)) vs. Matric Potential:

    • Graph Analysis: As matric potential decreases (soil gets drier), unsaturated hydraulic conductivity (K(\Psi)) dramatically decreases for both sandy loam and clay soil.

    • Sandy Soil: At wet conditions (near saturation), sandy soil has higher K(\Psi). However, as it dries, its larger pores empty quickly, leading to a rapid and dramatic decrease in K(\Psi). The connectivity is lost sooner.

    • Clay Soil: At wet conditions, clay soil has lower K(\Psi)) than sandy soil due to smaller pores. But as the soil dries, its smaller, numerous pores retain connectivity longer. Hence, under very dry conditions (e.g., below -10 kPa), clay soil can have higher K(\Psi)) than sandy soil.

    • Crossover Point: The lines for sandy and clay soil often cross around -10 kPa, indicating a shift in which texture conducts water faster at different moisture levels.

  • Summary of Water Flow vs. Soil Texture:

    • Coarse Material (Sandy):

      • Larger pore size but lower total porosity.

      • Faster flow when saturated or near saturation.

      • Much lower flow when dry (dries out quickly).

    • Fine Texture (Clay):

      • Smaller pore size but higher total porosity.

      • Slower flow under saturated conditions.

      • Faster flow compared to sandy soil at the dry end of the matric potential range (still much slower than saturated flow).

Preferential Flow in Unsaturated Conditions

  • Fingering: Even in uncracked soils, water may move in specific, distinct pathways (fingers), rather than uniformly.

  • Reasons for Fingering: Can be caused by hydrophobic conditions in the top layer (e.g., due to organic matter, fire, waxy coatings).

  • Implications:

    • Contaminant Transport: If contaminants are in the upper soil layer, preferential flow paths can quickly transport them to the groundwater table, bypassing the slower bulk matrix flow.

    • Fertilizer Management: Fertilizers applied to the surface can dissolve and be lost rapidly through preferential flow to groundwater if not mixed into the soil.

Wetting Patterns and Irrigation

  • Importance: Understanding wetting patterns is crucial for efficient irrigation.

  • Observation: Sandy loams exhibit a much narrower, deeper wetting pattern compared to clay loams, which have a wider, more lateral wetting pattern.

  • Explanation:

    • Sandy Soil: Gravimetric water potential dominates, pulling water predominantly downwards. There is less lateral movement due to weaker matric forces.

    • Clay Soil: Matric water potential (suction) is stronger and plays a more significant role. It pulls water more effectively to the side, distributing it wider, even though the overall movement might be slower.