(5) soil and infiltration

(apparently) jenny equation for soil formation

S = f(cl,o,r,p,t)

→ soil is a function of the 6 variables
climate, organisms, relief, parent material, time

what are some main conponents of soil

soil texture classes (3)

• sand

• silt

• clay

→ size of individual grains (particle size) → levels of infiltraiton

properties of soil: 3 phase system

Volume and Mass of: air, water solids

formulas for 3 phase system

• particle density: how dense the solid material is (excluding pore spaces)

• bulk density: mass of dry soil/total soil volume

• porosity: pore spaces

• volumetric water content: how much water is in the soil

• gravimetric water content: ratio of mass between water & solids

• relative saturation: how saturatedsoil is, how much water is this soil holding in relation to how much it can possibly hold

  • if void space V_f is totally filled by water → fully saturated

what is volumetric water content?

the volume of water contained in a given total volume of soil

→ tells what fraction of soil’s total volume is occupied by water

θ = V_w/V_t

_{Vw = volume of water in soil}

_{Vt = total volume of the soil sample}

→ the total soil volume includes both solid soil particles AND pore spaces

→ often expressed as m³

soil moisture measurement methods (5)

1. gravimetric

2. neutron scattering

3. di-electric constant methods

4. electrical conductance

5. tensiometry

1. gravimetric - soil moisture measuring

• taking soil sample → weigh → oven dry → reweigh

  • gives moisture content

• θ: volumetric soil moisture content

• p_w: constant (1000 kg/m³)

• volume of soil sample: using samping container of known volume

2. neutron scattering - soil moisture measuring

• neutrons emitted from radioactive source → scattered by water molecules

• rate of return of neutrons to probe = water content of soil (both liquid and solid!!!!)

3. di-electric constant - soil moisture measuring

• measuring propagation of an electrical signal through soil

  • time domain reflectometry (TDR)

  • frequency domain reflectometry (FDR)

    • aka capacitance probes

  • only records liquid water content

4. tensiometry - soil moisture measuring

• measures water pressure content

• provides indirect measure of soil moisture changes

  • moisture content in an unsaturated soil is related to water pressure

  • soil moisture retention curve

→ pressure to determine… amount of suction required (pressure) to calculate water in soil

→ more pressure = less moisture/less saturated

soil water potential: instruments

→ potential energy in soil

• tensiometer

• well

• piezometer

• but first, soil water potential (by way of hydraulic head)

what is hydraulic head (h)

• measures amount of total energy associated with water at certain depths

  • potential of water to move across a space

  • soil water potential

→ water droplets in relation to surface distance (depth)

• elevation head and pressure head

well

• water level inside well indicates depth of the water table

  • difference in pressure in stuff directs water towards well

piezometer

• pressure & sucking measurement tool

• measures height to which a column of fluid rises against gravity, or groundwater pressure

• Water moves until the hydraulic head inside the tube matches the hydraulic head in the surrounding soil

  • matching hydraulic head (at equilibrium, no flow)

piezometer and equilibrium

• assume hydrostatic equilibrium in the piezometer

  • h_D = h_C

• assume water in piezometer is in equilibrium with soil water at B

  • h_C = h_B

soil water movement

A= cross sectional area (m²)

V = volume of water draining through A in a time interval Δt (m³)

Q = discharge rate = V/Δt (m³/s)

q = flux rate = V/(A× Δt) (or = Q/A) (m/s)

→ water always moves from higher h to lower h

→ high pressure/energy to low pressure/energy

darcy’s law

• water flow rate is proportional to hydraulic head gradient in the direction of flow

• water flow depends on the soil's ability to transmit water and the difference in hydraulic head over a distance
  
  

• Larger hydraulic head difference over the same distance → faster flow.

• Shorter distance with the same head difference → faster flow.

darcy’s law equation

→ describes flow of a fluid through a prorous medium (how easily and how quickly)

q = -K × ΔH/ΔL

what variables make up darcy’s law?

• q = Water flux: How much water flows through a given area (m/s).

• K = Hydraulic conductivity: How easily water moves through soil (sand = high, clay = low).

• Δh = Change in hydraulic head: Difference in hydraulic head between two points (m).

• ΔL = Distance: Distance between the two points (m).

• (-) = Indicates that water flows from higher to lower hydraulic head.

darcy’s law equation vertical flow vs downslope flow

Vertical flow	Downslope flow

Water moves up or down.

Water moves sideways along a slope.

Uses vertical distance, Δz

Uses distance along the slope, L.

Uses vertical hydraulic conductivity, Kz.

Uses hydraulic conductivity, K, in the direction of flow.

Includes a negative sign to indicate flow direction.

Uses the absolute head difference to calculate the magnitude of flow.

darcy’s law: K

• K = hydraulic conductivity

  • how easily pore fluid escapes from compacted pore space

• saturated hydraulic conductivity: K =

  • r_f = density of fluid (kg m^-3)

  • g = gravitational acceleration (m s^-2) → constant

  • k = intrinsic permeability (m²) → given value

  • µ = dynamic viscosity of fluid (k m^-1 s^-2)

→ higher K = easier water movement

example: groundwater flow between 2 points

	point A	point B
elevation, z	120 m	105 m
pressure head ψ	8 m	18 m
L= 500 m

key concept: water flows down the hydraulic head gradient (not always from higher elevation to lower elevation)

answer: 2 ×10^-6 m/s (slow!!)

darcy’s law, relationship between saturated hydraulic conductivity vs temp

surplus of water in soil

• reaches field capacity (amount of water soil can hold after excess water drains away), extra warer leaves in two ways

  • Deep percolation: Water drains downward past plant roots into deeper soil.

  • Evapotranspiration (ET): Water returns to the atmosphere through evaporation from soil and water released by plants.

water surplus vs water deficit

• P > PET = surplus (too much water coming in).

• P < PET = deficit (not enough water coming in).

P = precipitation, input

PET = potential evapotranspiration, how much water could evaporate from ground

soil infiltration

• permeation of liquid into something by filtration

• infiltration rate (f): rate at which water enters a soil at the surface

  • infiltrability (f_c): infiltration capactiy. maximum rate at which water can enter a soil

    • impacted by soil type, compaction, input intensity, previous conditions of soil (dry/wet)

soil infiltration: infiltration rate and precipitation relationship

soil infiltration measurement types

• ring infiltrometer

  • infiltration measured in inner ring. rates are all known, isolates infiltation rate of confined vertical area

• sprinkling experiments

  • water sprinkled at rate that exceeds infiltrability

  • excess flows over surface → captured and measured

  • infiltrability: difference between the sprinkling rate and rate of overland flow production

hortons equation

know briefly

• describes how the infiltration capacity of soil decreases over time during rainfall

phillips equation

briefly

• how water infiltrates into soil over time

  • infiltration changes over time as soil becomes wetter (infiltration decreases)

• infiltration eventually reaches steady state

soil infiltration: green and ampt theory

• how water infiltrates into soil during rainfall, assuming a relatively sharp boundary between wet soil above and drier soil below

green and ampt theory in relation to darcy

Green-Ampt uses Darcy's Law to estimate infiltration capacity based on soil conductivity, capillary suction, and wetting-front depth.

green- ampt theory: how does infiltration change over time

• Early in rainfall: Capillary suction pulls water into the soil, creating a strong pressure head gradient. Infiltration is high.

• Later in rainfall: The wetting front moves deeper, reducing the effect of capillary suction. Infiltration decreases.

• Eventually: Gravity becomes the main force driving water downward, and the infiltration rate approaches the saturated hydraulic conductivity (K_s).

Remember: Infiltration starts high and decreases over time until it approaches K_s, as the influence of capillary suction decreases and gravity becomes dominant.

green and ampt theory: example calculations HUGE!!!

soil moisture balance

• accounting of water entering, leaving, and being stored in soil over time

  • tells us if soil is gaining, losing, or maintaining water storage

• Water inputs: Precipitation (rain and snowmelt).

• Water outputs: Evapotranspiration, runoff, and drainage into deeper soil.

• Water storage: Water retained in the soil for later use by plants.