[L3] Solid water storage & percolation / EEE

Unsaturated zone

• portion of the subsurface above of the groundwater table

• rock and soil contains air as well as water in its pores

• important capacity to distribute the incoming flux of precipitation into 3 outgoing fluxes: overland flow, recharge & evapo(transpi)ration + provides water storage capacity

Soil

• most active part of the unsaturated zone

Formed by both:

• disintegration and decomposition of rocks by physical and chemical processes

• activity and accumulation of residues of numerous plants and animals

→ is a complex mixture of solids (rock + organic material), liquids and gases

Density of solids (Soil Hydrophysical properties)

Dry bulk density (Soil Hydrophysical properties)

Total bulk density (Soil Hydrophysical properties)

Porosity (Soil Hydrophysical properties)

Void ratio (Soil Hydrophysical properties)

Interrelating formula (Soil Hydrophysical properties)

Volumetric moisture content

• apply to soil & underlying (unconsolidated & consolidated sediments & rocks)

Gravimetric moisture content

• apply to soil & underlying (unconsolidated & consolidated sediments & rocks)

Interrelating water / moisture content formula

• apply to soil & underlying (unconsolidated & consolidated sediments & rocks)

Types of porosity

• structure determines porosity & other hydraulic properties

Categories of hydraulic properties

physical properties = easy to obtain → need soil hydraulic properties to understand movement and storage of water & solutes

2 categories:

• Storage

• Transmission

Storage

the soil moisture characteristic, 𝜃(𝜓)

→ how much water the soil holds at a given matric potential; also called the water retention curve

𝜃 = volumetric moisture content

𝐾 = hydraulic conductivity

𝜓 = the matric potential (< 0) or matric suction (> 0)

Transmission

the hydraulic conductivity function, 𝐾(𝜓)

how readily the soil passes water at a given matric potential; it falls steeply as the soil dries

𝜃 = volumetric moisture content

𝐾 = hydraulic conductivity

𝜓 = the matric potential (< 0) or matric suction (> 0)

Energy of water in the soil

• fluid potential for flow through porous media = mechanical energy per unit mass of fluid

Water flows region of high potential → low potential

• In soil → determined by potential, kinetic and elastic energy

• In unsaturated zone → kinetic & elastic energy can be neglected.

Forces that determine potential energy

Capillarity

• a result of the surface tension at the interface between soil air, soil water and solids

Adsorption

• on the surfaces of soil particles, due to electrostatic forces attaching the polar water molecules to the charged faces of the solids

Osmosis

• from solutes in the water - much less important, but can matter (e.g. saline water around roots)

Gravity

Soil water potential

potential energy of soil water relative to water in a standard reference state

(determined by combination of capillary, adsorption, osmosis & gravity)

Capillarity

• definition

• formula

Tendency of a liquid in a capillary tube to rise or fall as a result of differences in surface tension between the solid/liquid and the solid/gas interface.

Most solids: solid/water interface surface tension < solid/air interface → water is “pulled up” against gravity

Soil matric potential

Potential energy of water related to capillary retention p_m Pa[𝑀𝐿⁻¹𝑇⁻²].

• also expressed as head of water m [L]

Soil pore spaces = analogous to capillary tubes → soil retains water against the force of gravity

Effect decreases rapidly w/ increasing radius → water is retained more strongly in small pores than in large ones

Pressure head associated w/ capillarity is always negative relative to the reference position outside the soil → can be referred to as matric suction (> 0)

Soil moisture characteristic (= water retention curve)

Empirical relation between 𝜓 (a function of the soil pore size distribution) & volumetric water content 𝜃.

Wilting point

the maximum suction that plants can apply to extract water from the soil (around 15 bar or 15000 cm)

Field capacity

excess water has drained away; beyond this point the soil will not drain further because retention forces exceed the gravitational force (0.33 bar or 330 cm)

Saturation point

The maximum soil water content; all pores are filled (0 bar or 0 cm).

Matric suction = 0

the soil is completely saturated (e.g. after a rain event) → the soil volume is entirely filled with water and solids.

External force is applied → air gradually replaces the water

• water w/ the lowest retention (in the largest pores) is released first

Movement of soil water

Soil water moves from regions of high total potential → regions of lower potential

Driving force = gravity while water is retained by the matric potential

Hydraulic head

Potential mechanical energy per unit weight of fluid relative to a datum.

Darcy’s law, unsaturated

hydraulic head related to flux of water through the soil

where 𝐾(𝜃) is the hydraulic conductivity [𝐿𝑇−1]

∇ℎ the hydraulic head gradient in three dimensions

In saturated conditions → 𝐾(𝜃) = the saturated conductivity 𝐾_𝑠

At the soil surface → is the soil’s infiltration capacity

𝑞 is a flux through bulk area, not the speed of the water: the water itself moves faster, 𝑣_𝑝 = 𝑞/𝑛_e

Hydraulic conductivity & matric potential

water moves quicker through larger pores than smaller pores

suction applied → larger pores empty first → forces water to flow through smaller pores

shape of curve depends on pore distribution → sandy soils usually have larger pores than clayey soils therefore higher conductivity near saturation

curve is empirical → can’t be derived analytically

Macroscopic implications

Flow in the unsaturated zone = predominantly vertical under the influence of gravity → recharges the saturated zone, causing the water table (= phreatic surface) to move

→ may cause pressure gradients which force water to flow horizontally

Generation of overland flow

1. No overland flow

2. Infiltration-excess: rainfall intensity i > infiltration capacity f

3. Saturation-excess: rain falls on the ground already saturated from below

Contribution to stormflow & baseflow

quickflow = rainfall slides over ground

baseflow = rainfall infiltrates

Model of the unsaturated zone

Gravimetric determination (Measuring of soil water)

1. a soil sample of known volume (𝑉𝑇) is removed from the ground w/ a soil auger

2. sample is weighed (𝑀_𝑇)

3. sample is then dried in an oven w/ the temperature controlled between 100 and 110∘C until the final weight (𝑀𝑆) is constant

4. calculate 𝜃_G

5. calculate dry bulk density 𝜌_𝑑 = 𝑀_𝑆 / 𝑉_T

6. knowing pw (1gcm^-3) volumetric water content 𝜃 can be calculated

Time domain reflectometry (TDR)

originally developed to detect faults in electric cables → now a widely applied method to measure soil moisture

• dielectric constant of soil depends strongly on its water content ← is determined from the travel time of an electromagnetic wave along two or more parallel metal rods in the soil

• main advantage = TDR already integrates 𝜃 over the length of the probe

Field methods

Experimental design to measure overland flow as a proportion of precipitation.

• Vertical plates isolate a plot so that neither overland nor subsurface flow enters it from outside

• Gutters at the foot collect what leaves it