Soil Water (Vadose Zone)

Infiltration - movement of water from soil surface to soil

Capillary rise - movement from saturated zone upwards into unsat zone by surface tension

Recharge - movement of water into the saturated zone (groundwater recharge)

Interflow - flow in the unsat zone downslope

Percolation - downward flow in unsat zone

Understanding infiltration and redistribution important for e.g.:1. 2. movement of nutrients, pollutants, etc. 3. estimating timing and amounts of ground-water recharge4. Predicting stream response to snowmelt and rainfall

Infiltration and redistribution involve unsaturated flow in a porous media (soil). Therefore, first must understand the nature of the porous media

P < 0

P > 0

Soil Properties

Soil matrix composed of rock, air, water, and organic matter. To simplify things organic matter is often not considered, but does contribute to the soil hydraulic properties.

Size of pores in soil ~= to grain sizesoil is a mixture of grain sizessoil texture is a term used to describe the grain size distribution (by weight), less than 2mm (upper boundary for sand)

Measurement - silt/clay measured by settling techniques (pipette analysis, sedigraph, lpsa)

Stoke’s Law

V = 2r2g(ρparticle – ρmedium) 9γ

viscosity

Fine earth fraction (soil)

Particle density (ρm) is a weighted average density of mineral grains. Can be measured by displacement techniques

where Ws is the mass and Vs is the volume of the mineral grains

in practice this is difficult so usually assumed to be around 2.65 g cm-3

Bulk Density (b)

Weight of unit volume of soil after oven-drying at 105oC for 24 hrs

In almost all cases we discuss dry bulk density, but in rare occasions we might be interested in the wet bulk density (bulk density in it’s natural state with a given amount of soil moisture)

b = Ws/V = Ws/(Va + Vw + Vs)

Porosity (n)Proportion of pore spaces in a volume of soil

Like bulk density is constant over time in most cases, and decreases with depth (compaction down deep + biological cavities shallow)

- In general finer-grained soils have higher porosities-Organic material can increase the porosity of a soil dramatically- porosity increases with sorting

n = (Va + Vw)/V = Vv/V

Void Ratio

e = Vv/Vs

Volumetric Water Content (θ)(or simply “soil moisture”)

ratio of water volume to soil volume

ranges from 0 (dry) to n (saturated)

Can be measured at the same time as bulk density when drying

Non-destructive techniques for monitoring field conditions include:1. Electrical resistance blocks - measures resistance in an artifical block of porous material inserted in the soil profile2. Neutron moisture meters - detect scattering of neutrons by hydrogen atoms3. Gamma-ray scanners - measure absorption of gamma rays by waterPassive microwave techniques being developed so that soil moisture can be measured remotely. Resolution would only be a few square km’s

Gravimetric Water Content

θg = 100(Ww/Ws)

Ww is the weight of water in the soil, Ws is the weight of solid particles

Degree of Saturation (S)(or “wetness”)

Hydraulic properties of soils

Darcy’s Law defines flow in porous media

Darcy’s Law is

where: Vx is the volumetric flow rate in the x direction per unit x-sectional area of soilz is height above some arbitrary datump is water pressure (measured in relation to atmospheric…gage pressure)γw is weight density of waterKh is the hydraulic conductivity (or “permeability”) of the soil or ability of the soil (or rock) to conduct water through it. A rate that depends on textural properties in saturated conditions, or textural + 2 in unsaturated conditions

dz/dx is the gradient of gravitational potential energy per unit weight of flowing water

d(p/γw)/dx is the gradient of pressure-potential energy

V Kd z p

dxx hw

( / )

Since γw is effectively constant for situations that do not involve major gradients in temperature and salinity, we can express the pressure-potential energy as pressure head (hp)

In unstaturated conditions both pressure head and hydraulic conductivity depend on soil moisture so Darcy’s Law for unsaturated flow becomes:

Vx = -K(θ) d[z + hp(θ)] dx

n

Soil-Water Pressure

- Pressure is force per unit area P=F/A- conventionally measured in relation to atmospheric (gage)

p>0 and hp>0 in saturated flowsp<0 and hp <0 in unsaturated flows

- Negative pressure is “tension” or “suction”- When hp goes below zero it is called “tension head” or “moisture potential”

Fetter denotes moisture potential as Ψ

In unsaturated soils, water is held to grains by surface-tension forces and p and Ψ will always be negative

tension inversely proportional to the radius of capillary tubes (pores) and proportional to the radius of curvature of menisci

therefore tension increases as soils get drier, and tension is higher in silty soils than in sandy soils

hc = 2σcosλ/ρgr

σ is surface tension of fluidr is the radius of capillary tube

What is ρg?Now simplify for soils hc = 2σcosλ/ρgr

Capillary fringe is not an even surface

Measurement of tension can be done directly using:

1. Tensiometers- practical range covers coarse soils only (lower tensions) - use of several at different depths can get hydraulic gradients

Relation between pressure head and water content for a given soil is called the Moisture-Characteristic Curve

- curves for different soil types constructed on soil samples in the lab

2. Thermocouple psychrometers- measures soil-water tension using transfer equations based on the humidity of soil air- at equilibrium potential of soil moisture is proportional to the relative humidity-wet bulb and dry bulb temperature measured and RH calculated

Relationship between Soil RH and tension is:

Where R is the gas constant (8.31 J/mol K), Ta is the Kelvin temperature of the air, and M is the molecular weight of water.

Fetter’s“Moisture Potential”

Hysterisis

- Problem arises because tension of the soil for a given water content is not unique, but depends on the soils history of wetting and drying- hysterisis still a largely mysterious phenomenon with many competing theories

-- during wetting the small pores fill first and during draining the large pores empty first-others include:

1. Meniscus radii is greater in an advancing fluid than in a retreating one

2. Entrapped air in a newly wetted soil decreases water content per unit suction

3. Clay-rich soils change geometry through swelling and shrinking during wetting and drying

- As a standard, the draining (desorption) curve is the one used

Water Conditions in Natural Soils

Field Capacity (θfc) is defined as the amount of water in a soil after initial draining causes the soil to reach a state of quasi-equilibrium, after which removal of water only occurs very slowly

- this is the water that can be held against the force of gravity- pressure head for all soils ~-340 cm for all soils- at this point water can only be removed by evapotranspiration- θfc for sands is as low as 0.1 and >0.3 for clays

- plants can only exert a suction of about -15,000 cm and when water content (tension) exceeds this value the Permanent Wilting Point has been reached-

Available water content (θa) is the difference between field capacity and the permanent wilting point

Hygroscopic water is water that is in equilibrium with the surrounding atmosphere. Can only be removed through application of high heat in the lab for prolonged periods. - in clay-rich soils, even drying for 24 hours at 105oC may leave behind some water that is strongly attracted to the clay particles

Pedologic Horizons

-

- sequence of horizons makes up the soil profile- horizons delimited by color, texture, organic matter, the degree of deposition (illuviation) or removal (eluviation) of material by physical and chemical processes- development of horizons dependant on climate, topography, disturbances (erosion, deposition), parent material, and duration of horizon development

PressureTension

θpwp < θ < n

θfc < θ < n

θ = n

θ = n

Hydrologic Horizons

Hydrologic Horizons

- horizons defined by water content and pressures

Ground-Water Zone (phreatic zone)

- saturated with + pressure- if no flow, pressure is only hydrostatic

p iszo is the height of the water tableγw is weight density of water

p z z zw o( ) ( )

Capillary Fringe (tension-saturated zone)- lowest portion of the vadose zone saturated or near-saturated due to capillary rise of ground-water- pressures will be negative even if saturatedWe can approximate r with the average grain size of the soil

so

for most soils so that all we need to know is something about the temperature and texture at depth to calculate hcr (assuming relatively fresh water)

-

hrcr

w

2

Intermediate Zone

- zone where water largely enters by percolation from above and leaves by gravity drainage- moisture content will increase after heavy rains and return to field capacity after a while- tensions >θae -

- may not exist in certain situations (e.g. wetlands in shallow bedrock regions)

Root Zone (Soil Moisture Zone)

- top is soil surface and bottom is depth to which plants can extract water- water enters by infiltration and leaves by evapotranspiration or gravity drainage- water content above permanent wilting point- below field capacity much of the time between rainfall events

Comparison of pedologic and hydrologic zones

- root zone usually extends into zone of eluviation and may occupy entire solum- solum usually developes above capillary fringe, but water table may move into solum seasonally- gleying is a blue/grey/green mottling of soil that indicates soil below water table for long periods of time-Impervious and semi-impervious layers in the soil profile can created “perched” water tables

Infiltration

Infiltration rate f(t) - rate at which water passes from the surface to the soil

Water-input rate w(t) - rate of delivery of water to the soil surface (i.e. rain or snowmelt)

Infiltration capacity fc(t) - maximum f(t) possible for a given soil

Depth of ponding Y(t) - depth of water standing on the surface

MeasurementRing Infiltrometers

-metal rings inserted in soil to which water is added at recorded rate- infiltration rates usually start high and settle to a constant lower rate which is taken as the infiltration capacity- fc(t) in this case is . the saturated hydraulic conductivity of surface soil

- reduction of lateral movement by double ring, or adjust single ring values

-

Sprinkler Plot Studies- apply artificial rainfall to an experimental plot and record the amount that doesn’t infiltrate and runs off

f(t) = w - q(t)

Soil-Water changes

- install e.g a series of tensiometers to measure change in hydraulic gradient and relate that to infiltration rate if w is known or controlled

Factors affecting infiltration rate

1.

2. Saturated hydraulic conductivity- vegetation, burrowing fauna, etc. at surface tends to increase K- leaf litter can have opposite effect- freezing of wet surface greatly reduces K- clays shrink and swell- raindrop compaction- human intervention: tilling, paving, etc.

3. Soil moisture at start of water input- left over moisture from previous events- raised water table

4. Roughness and inclination of surface- only important to infiltration rates during ponding- steep slopes and smooth surfaces remove water faster (and lower infiltration rates overall

5 chemical characteristics of surface-

6. Physical and chemical characteristics of water- Salinity and temperature of water affect tension, density, and viscosity- K significantly increases with increasing temperature and decreasing salinity

Modeling Infiltration

Richards Equation

- basic theoretical equation for vertical unsaturated flow in a homogeneous porous medium

- numerical solutions and require detailed data usually not available, so:

Green-and-Ampt Model

- model based on Darcy’s Law and the principal of conservation of mass- basic model assumes we are dealing with a block of soil that is homogeneous to an indefinate depth (porosity, and sat. hydraulic conductivity are consistant throughout- no water table, capillary fringe, or impermeable layer- horizontal surface with no evapotranspiration and no ponding at t0- initial moisture in entire profile at t0 is considerably below field capacity-water is delivered to the surface by rainfall or snowmelt at a rate of w and continues for a duration of tw

K

z zK

z th

h

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